On numerical solution of the Gardner Ostrovsky equation

Article

Obregon, M. A. and Stepanyants, Y. A.. 2012. "On numerical solution of the Gardner Ostrovsky equation." Mathematical Modelling of Natural Phenomena (MMNP). 7 (2), pp. 113-130. https://doi.org/10.1051/mmnp/20127210

Article Title	On numerical solution of the Gardner Ostrovsky equation
ERA Journal ID	32402
Article Category	Article
Authors	Obregon, M. A. (Author) and Stepanyants, Y. A. (Author)
Journal Title	Mathematical Modelling of Natural Phenomena (MMNP)
Journal Citation	7 (2), pp. 113-130
Number of Pages	18
Year	2012
Place of Publication	Les Ulis, France
ISSN	0973-5348
	1760-6101
Digital Object Identifier (DOI)	https://doi.org/10.1051/mmnp/20127210
Web Address (URL)	http://www.mmnp-journal.org/action/displayAbstract?fromPage=online&aid=8503520
Abstract	A simple explicit numerical scheme is proposed for the solution of the Gardner–Ostrovsky equation which is also known as the extended rotation-modified Korteweg–de Vries (KdV) equation. This equation is used for the description of internal oceanic waves affected by Earth' rotation. Particular versions of this equation are also known in numerous applications. The proposed numerical scheme is a further development of the well-known finite-difference scheme earlier used for the solution of the KdV equation. The scheme is of the second order accuracy both on temporal and spatial variables. The stability analysis of the scheme is presented for infinitesimal perturbations. The conditions for the calculations with the appropriate accuracy have been found. Examples of calculations with the periodic boundary conditions are presented to illustrate the robustness of the proposed scheme.
Keywords	KdV equation; Ostrovsky equation; solution; terminal decay; Petviashvili method; numerical scheme
ANZSRC Field of Research 2020	490303. Numerical solution of differential and integral equations
	490299. Mathematical physics not elsewhere classified
	490199. Applied mathematics not elsewhere classified
Public Notes	File reproduced in accordance with the copyright policy of the publisher/author.
Byline Affiliations	University of Malaga, Spain
	Department of Mathematics and Computing
Institution of Origin	University of Southern Queensland

Permalink -

https://research.usq.edu.au/item/q1492/on-numerical-solution-of-the-gardner-ostrovsky-equation

Download files

Published Version

	Obregon_Stepanyants_MMNP_2012_PV.pdf
File access level: Anyone

1967
total views
450
total downloads
9
views this month
1
downloads this month

Export as

Related outputs

Highly localized horseshoe ripplons and solitons in positive dispersion media

Zhang, Zhao, Guo, Qi and Stepanyants, Yury. 2024. "Highly localized horseshoe ripplons and solitons in positive dispersion media." Wave Motion. 128. https://doi.org/10.1016/j.wavemoti.2024.103326

Long wave propagation in canals with spatially varying cross-sections and currents

Churilov, Semyon and Stepanyants, Yury. 2024. "Long wave propagation in canals with spatially varying cross-sections and currents." Nonlinear and Modern Mathematical Physics (NMMP 2022). Tallahassee, United States 17 - 19 Jun 2022 United States. Springer. pp. 19-79 https://doi.org/10.1007/978-3-031-59539-4_2

Localized wave structures: Solitons and beyond

Ostrovsky, L., Pelinovsky, E., Shrira, V. and Stepanyants, Y.. 2024. "Localized wave structures: Solitons and beyond." Chaos: an interdisciplinary journal of nonlinear science. 34. https://doi.org/10.1063/5.0210903

Frequency downshifting in decaying wavetrains on the ocean surface covered by ice floes

Slunyaev, A. V. and Stepanyants, Y. A.. 2024. "Frequency downshifting in decaying wavetrains on the ocean surface covered by ice floes." Physics of Fluids. 36 (3). https://doi.org/10.1063/5.0200538

Solitons and lumps in the cylindrical Kadomtsev–Petviashvili equation. II. Lumps and their interactions

Zhang, Zhao, Hu, Wencheng, Guo, Qi and Stepanyants, Yury. 2024. "Solitons and lumps in the cylindrical Kadomtsev–Petviashvili equation. II. Lumps and their interactions." Chaos: an interdisciplinary journal of nonlinear science. 34 (1). https://doi.org/10.1063/5.0175716

Solitons and lumps in the cylindrical Kadomtsev–Petviashvili equation. I. Axisymmetric solitons and their stability

Hu, Wencheng, Zhang, Zhao, Guo, Qi and Stepanyants, Yury. 2024. "Solitons and lumps in the cylindrical Kadomtsev–Petviashvili equation. I. Axisymmetric solitons and their stability." Chaos: an interdisciplinary journal of nonlinear science. 34 (1). https://doi.org/10.1063/5.0175696

Scattering of gravity-capillary waves on a bottom step

Meylan, M.H. and Stepanyants, Y.A.. 2024. "Scattering of gravity-capillary waves on a bottom step." Physics of Fluids. 36 (1). https://doi.org/10.1063/5.0181237

Dynamics of Benjamin-Ono Solitons in a Two-Layer Ocean with a Shear Flow

Negi, Pawan, Sahoo, Trilochan, Singh, Niharika and Stepanyants, Yury. 2023. "Dynamics of Benjamin-Ono Solitons in a Two-Layer Ocean with a Shear Flow." Mathematics. 11 (15). https://doi.org/10.3390/math11153399

Creation of weakly interacting lumps by degeneration of lump chains in the KP1 equation

Zhang, Zhao, Guo, Qi and Stepanyants, Yury. 2023. "Creation of weakly interacting lumps by degeneration of lump chains in the KP1 equation." Chaos, Solitons and Fractals. 170, pp. 1-13. https://doi.org/10.1016/j.chaos.2023.113398

Analysis of internal solitary waves in the Gulf of Oman and sources responsible for their generation

Koohestani, Kamran, Stepanyants, Yury and Allahdadi, Mohammad Nabi. 2023. "Analysis of internal solitary waves in the Gulf of Oman and sources responsible for their generation." Water: an open access journal. 15 (4), pp. 1-28. https://doi.org/10.3390/w15040746

Solitary waves and their interactions in the cylindrical Korteweg–de Vries equation

Hu, Wencheng, Ren, Jingli and Stepanyants, Y.. 2023. "Solitary waves and their interactions in the cylindrical Korteweg–de Vries equation." Symmetry. 15. https://doi.org/10.3390/sym15020413

Interaction of internal solitary waves with long periodic waves within the rotation modified Benjamin-Ono equation

Grimshaw, R. H. J., Smyth, N. F. and Stepanyants, Y. A.. 2021. "Interaction of internal solitary waves with long periodic waves within the rotation modified Benjamin-Ono equation." Physica D: Nonlinear Phenomena. 419, pp. 1-10. https://doi.org/10.1016/j.physd.2021.132867

Multi-lump formations from lump chains and plane solitons in the KP1 equation

Zhang, Zhao, Yang, Xiangyu, Li, Biao, Guo, Qi and Stepanyants, Yury. 2023. "Multi-lump formations from lump chains and plane solitons in the KP1 equation." Nonlinear Dynamics. 111 (2), p. 1625–1642. https://doi.org/10.1007/s11071-022-07903-8

Peculiarities of resonant interactions of lump chains within the KP1 equation

Zhang, Zhao, Li, Biao, Chen, Junchao, Guo, Qi and Stepanyants, Yury. 2022. "Peculiarities of resonant interactions of lump chains within the KP1 equation." Physica Scripta: an international journal for experimental and theoretical physics. 97 (11), pp. 1-14. https://doi.org/10.1088/1402-4896/ac99aa

Complex Dynamics of Solitons in Rotating Fluids

Ostrovsky, Lev A. and Stepanyants, Yury A.. 2022. "Complex Dynamics of Solitons in Rotating Fluids." Volchenkov, Dimitri and Machado, J. A. Tenreiro (ed.) Mathematical Methods in Modern Complexity Science. Switzerland. Springer. pp. 63-78

Lump Interactions with Plane Solitons

Stepanyants, Yu. A., Zakharov, D. V. and Zakharov, V. E.. 2022. "Lump Interactions with Plane Solitons." Radiophysics and Quantum Electronics. 64 (10), pp. 665-680. https://doi.org/10.1007/s11141-022-10169-0

Modulation property of flexural-gravity waves on a water surface covered by a compressed ice sheet

Slunyaev, A. V. and Stepanyants, Y. A.. 2022. "Modulation property of flexural-gravity waves on a water surface covered by a compressed ice sheet." Physics of Fluids. 34. https://doi.org/10.1063/5.0100179

Assessment and Prediction of Sea Level Trend in the South Pacific Region

Raj, Nawin, Gharineiat, Zahra, Ahmed, Abul Abrar Masrur and Stepanyants, Yury. 2022. "Assessment and Prediction of Sea Level Trend in the South Pacific Region." Remote Sensing. 14 (4), pp. 1-25. https://doi.org/10.3390/rs14040986

Modulation Instability of Hydro-Elastic Waves Blown by a Wind with a Uniform Vertical Profile

Boral, Susam, Sahoo, Trilochan and Stepanyants, Yury. 2021. "Modulation Instability of Hydro-Elastic Waves Blown by a Wind with a Uniform Vertical Profile." Fluids. 6 (12), pp. 1-18. https://doi.org/10.3390/fluids6120458

Dynamics of internal envelope solitons in a rotating fluid of a variable depth

Stepanyants, Yury. 2019. "Dynamics of internal envelope solitons in a rotating fluid of a variable depth." Fluids. 4 (1), pp. 1-12. https://doi.org/10.3390/fluids4010056

Symmetric interactions of plane solitons in two-dimensional nonlinear lattices

Nikitenkova, Svetlana and Stepanyants, Yury. 2022. "Symmetric interactions of plane solitons in two-dimensional nonlinear lattices." Communications in Nonlinear Science and Numerical Simulation. 114, pp. 1-10. https://doi.org/10.1016/j.cnsns.2022.106602

Degenerate lump interactions within the Kadomtsev-Petviashvili equation

Zhang, Zhao, Li, Biao, Chen, Junchao, Guo, Qi and Stepanyants, Yury. 2022. "Degenerate lump interactions within the Kadomtsev-Petviashvili equation." Communications in Nonlinear Science and Numerical Simulation. 112, pp. 1-14. https://doi.org/10.1016/j.cnsns.2022.106555

Reflectionless wave propagation on shallow water with variable bathymetry and current. Part 2

Churilov, Semyon M. and Stepanyants, Yury A.. 2022. "Reflectionless wave propagation on shallow water with variable bathymetry and current. Part 2." Journal of Fluid Mechanics. 939, pp. 1-12. https://doi.org/10.1017/jfm.2022.208

Reflectionless wave propagation on shallow water with variable bathymetry and current

Churilov, Semyon M. and Stepanyants, Yury A.. 2021. "Reflectionless wave propagation on shallow water with variable bathymetry and current." Journal of Fluid Mechanics. 931, pp. 1-25. https://doi.org/10.1017/jfm.2021.935

Hydrodynamic models of astrophysical wormholes: the general concept

Churilov, Semyon and Stepanyants, Yury. 2021. "Hydrodynamic models of astrophysical wormholes: the general concept." Physics of Fluids. 33 (7). https://doi.org/10.1063/5.0056877

Transformation of envelope solitons on a bottom step

Ducrozet, Guillaume, Slunyaev, Alexey and Stepanyants, Yury. 2021. "Transformation of envelope solitons on a bottom step." Physics of Fluids. 33. https://doi.org/10.1063/5.0054806

Modulation instability of surface waves in the model with the uniform wind profile

Boral, Susam, Sahoo, Trilochan and Stepanyants, Yury. 2021. "Modulation instability of surface waves in the model with the uniform wind profile." Symmetry. 13. https://doi.org/10.3390/sym13040651

Can a submarine be perished by internal waves?

Stepanyants, Yu. A.. 2021. "Can a submarine be perished by internal waves?" Priroda (in Russian).

Hydrodynamic Forces Exerting on an Oscillating Cylinder under Translational Motion in Water Covered by Compressed Ice

Stepanyants Yury and Sturova, Izolda. 2021. "Hydrodynamic Forces Exerting on an Oscillating Cylinder under Translational Motion in Water Covered by Compressed Ice ." Water: an open access journal. 13 (6). https://doi.org/10.3390/w13060822

Description of Nonlinear Vortical Flows of Incompressible Fluid in Terms of a Quasi-Potential

Ermakov, Andrei and Stepanyants, Yury. 2021. "Description of Nonlinear Vortical Flows of Incompressible Fluid in Terms of a Quasi-Potential ." Physics. 3 (4), pp. 799-913. https://doi.org/10.3390/physics3040050

Waves on a compressed floating ice plate caused by motion of a dipole in water

Stepanyants, Yury and Sturova, Izolda V.. 2020. "Waves on a compressed floating ice plate caused by motion of a dipole in water." Journal of Fluid Mechanics. 907, pp. A7-1. https://doi.org/10.1017/jfm.2020.764

Emergence of envelop solitary waves from initial localised pulses within the Ostrovsky equation

Grimshaw, R. H. J. and Stepanyants, Y. A.. 2020. "Emergence of envelop solitary waves from initial localised pulses within the Ostrovsky equation." Radiophysics and Quantum Electronics. 63 (1), pp. 21-28. https://doi.org/10.1007/s11141-020-10031-1

The asymptotic approach to the description of two-dimensional symmetric soliton patterns

Stepanyants, Yury. 2020. "The asymptotic approach to the description of two-dimensional symmetric soliton patterns." Symmetry. 12 (10). https://doi.org/10.3390/sym12101586

A geometric model for estimating the volume and surface area of apples

Scarmana, Gabriel, McDougall, Kevin and Stepanyants, Yury. 2020. "A geometric model for estimating the volume and surface area of apples." Smart Surveyors for Land and Water Management (2020). Amsterdam, Netherlands 10 - 14 May 2020 Copenhagen, Denmark.

Kinematics of interacting solitons in two-dimensional space

Ostrovsky, L.A. and Stepanyants, Y. A.. 2020. "Kinematics of interacting solitons in two-dimensional space." Russian Journal of Earth Science. 20, pp. 1-11. https://doi.org/10.2205/2020ES000735

Nonlinear Models of Finite Amplitude Interfacial Waves in Shallow Two-Layer Fluid

Kurkina, Oxana, Kurkin, Andrey, Pelinovsky, Efim, Stepanyants, Yury and Talipova, Tatiana. 2019. "Nonlinear Models of Finite Amplitude Interfacial Waves in Shallow Two-Layer Fluid." Berezovski, Arkadi and Soomere, Tarmo (ed.) Applied Wave Mathematics II: Selected Topics in Solids, Fluids, and Mathematical Methods and Complexity. Cham, Switzerland. Springer. pp. 61-87

Nonlinear Waves in a Rotating Ocean (The Ostrovsky Equation and Its Generalizations and Applications)

Stepanyants, Yury. 2020. "Nonlinear Waves in a Rotating Ocean (The Ostrovsky Equation and Its Generalizations and Applications)." Russian Academy of Sciences, Izvestiya: Atmospheric and Oceanic Physics. 56 (1), pp. 16-32. https://doi.org/10.1134/S0001433820010077

Evolution of non-stationary pulses in a cold magnetized quark-gluon plasma

Fogaca, D. A., Fariello, R., Navarra, F. S. and Stepanyants, Y. A.. 2020. "Evolution of non-stationary pulses in a cold magnetized quark-gluon plasma." Communication on Nonlinear Sciences and Numerical Simulation. 83. https://doi.org/10.1016/j.cnsns.2019.105144

Transformation of Long Surface and Tsunami-Like Waves in the Ocean with a Variable Bathymetry

Ermakov, Andrei and Stepanyants, Yury. 2020. "Transformation of Long Surface and Tsunami-Like Waves in the Ocean with a Variable Bathymetry." Pure and Applied Geophysics. 177 (3), pp. 1675-1693. https://doi.org/10.1007/s00024-019-02259-4

Rossby waves in the ocean covered by compressed ice

Stepanyants, Y. A. and Sturova, I. V.. 2020. "Rossby waves in the ocean covered by compressed ice." Geophysical and Astrophysical Fluid Dynamics. 114 (3), pp. 306-316. https://doi.org/10.1080/03091929.2020.1712716

Soliton interaction with external forcing within the Korteweg–de Vries equation

Ermakov, Andrei and Stepanyants, Yury. 2019. "Soliton interaction with external forcing within the Korteweg–de Vries equation." Chaos: an interdisciplinary journal of nonlinear science. 29 (1). https://doi.org/10.1063/1.5063561

The effects of interplay between the rotation and shoaling for a solitary wave on variable topography

Stepanyants, Yury. 2019. "The effects of interplay between the rotation and shoaling for a solitary wave on variable topography." Studies in Applied Mathematics. 142 (4 (Special Issue)), pp. 465-486. https://doi.org/10.1111/sapm.12255

Helical solitons in vector modified Korteweg-de Vries equations

Pelinovsky, Dmitry E. and Stepanyants, Yury A.. 2018. "Helical solitons in vector modified Korteweg-de Vries equations." Physics Letters A. 382 (44), pp. 3165-3171. https://doi.org/10.1016/j.physleta.2018.08.015

Dynamics of particles and bubbles under the action of acoustic radiation force

Ostrovsky, Lev A. and Stepanyants, Yury A.. 2018. "Dynamics of particles and bubbles under the action of acoustic radiation force." Edelman, Mark, Macau, Elbert E. N. and Sanjuan, Miguel A. F. (ed.) Chaotic, fractional, and complex dynamics: New insights and perspectives. Germany. Springer. pp. 205-230

Modeling of Bose–Einstein condensation in a water tank

Rousseaux, Germain and Stepanyants, Yury. 2018. "Modeling of Bose–Einstein condensation in a water tank." Abcha, Nizar, Pelinovsky, Efim and Mutabazi, Innocent (ed.) Nonlinear waves and pattern dynamics. Cham, Switzerland. Springer. pp. 91-102

Adiabatic decay of internal solitons due to Earth’s rotation within the framework of the Gardner–Ostrovsky equation

Obregon, Maria, Raj, Nawin and Stepanyants, Yury. 2018. "Adiabatic decay of internal solitons due to Earth’s rotation within the framework of the Gardner–Ostrovsky equation." Chaos: an interdisciplinary journal of nonlinear science. 28 (3), pp. 1-11. https://doi.org/10.1063/1.5021864

Soliton solutions to the fifth-order Korteweg–de Vries equation and their applications to surface and internal water waves

Khusnutdinova, K. R., Stepanyants, Y. A. and Tranter, M. R.. 2018. "Soliton solutions to the fifth-order Korteweg–de Vries equation and their applications to surface and internal water waves." Physics of Fluids. 30 (2). https://doi.org/10.1063/1.5009965

Decay of Benjamin–Ono solitons under the influence of dissipation

Grimshaw, Roger H., Smyth, Noel F. and Stepanyants, Yury A.. 2018. "Decay of Benjamin–Ono solitons under the influence of dissipation." Wave Motion. 78, pp. 98-115. https://doi.org/10.1016/j.wavemoti.2018.01.005

Resonance properties of forced oscillations of particles and gaseous bubbles in a viscous fluid at small Reynolds numbers

Hassan, H. K. and Stepanyants, Y. A.. 2017. "Resonance properties of forced oscillations of particles and gaseous bubbles in a viscous fluid at small Reynolds numbers." Physics of Fluids. 29 (10). https://doi.org/10.1063/1.5002152

Particle dynamics in a viscous fluid under the action of acoustic radiation force

Hassan, Hassan K., Ostrovsky, Lev A. and Stepanyants, Yury A.. 2017. "Particle dynamics in a viscous fluid under the action of acoustic radiation force." Interdisciplinary Journal of Discontinuity, Nonlinearity, and Complexity. 6 (3), pp. 317-327. https://doi.org/10.5890/DNC.2017.09.006

Internal solitary waves in two-layer fluids at near-critical situation

Kurkina, O., Singh, N. and Stepanyants, Y.. 2014. "Internal solitary waves in two-layer fluids at near-critical situation." 19th Australasian Fluid Mechanics Conference (AFMC 2014). Melbourne, Australia 08 - 11 Dec 2014 Australia.

Decay of Kadomtsev–Petviashvili lumps in dissipative media

Clarke, S., Gorshkov, K., Grimshaw, R. and Stepanyants, Y.. 2018. "Decay of Kadomtsev–Petviashvili lumps in dissipative media." Physica D: Nonlinear Phenomena. 366, pp. 43-50. https://doi.org/10.1016/j.physd.2017.11.009

Multi-lump structures in the Kadomtsev–Petviashvili equation

Stepanyants, Yury. 2017. "Multi-lump structures in the Kadomtsev–Petviashvili equation." Aronson, Igor S., Pikovsky, Arkady, Rulkov, Nikolai F. and Tsimring, Lev S. (ed.) Advances in dynamics, patterns, cognition: challenges in complexity. Cham, Switzerland. Springer. pp. 307-324

Soliton spectra of random water waves in shallow basins

Giovanangeli, J.-P., Kharif, C. and Stepanyants, Y.A.. 2018. "Soliton spectra of random water waves in shallow basins." Mathematical Modelling of Natural Phenomena (MMNP). 13 (4), pp. 1-20. https://doi.org/10.1051/mmnp/2018018

Obliquely propagating skew KP lumps

Singh, N. and Stepanyants, Y.. 2016. "Obliquely propagating skew KP lumps." Wave Motion. 64, pp. 92-102. https://doi.org/10.1016/j.wavemoti.2016.03.005

Wave blocking phenomenon of surface waves on a shear flow with a constant vorticity

Maissa, Philippe, Rousseaux, Germain and Stepanyants, Yury. 2016. "Wave blocking phenomenon of surface waves on a shear flow with a constant vorticity." Physics of Fluids. 28 (3). https://doi.org/10.1063/1.4942116

Wave scattering in spatially inhomogeneous currents

Churilov, Semyon, Ermakov, Andrei and Stepanyants, Yury. 2017. "Wave scattering in spatially inhomogeneous currents." Physical Review D. 96 (6), p. 064016. https://doi.org/10.1103/PhysRevD.96.064016

Scattering of long water waves in a canal with rapidly varying cross-section in the presence of a current

Churilov, Semyon, Ermakov, Andrei, Rousseaux, Germain and Stepanyants, Yury. 2017. "Scattering of long water waves in a canal with rapidly varying cross-section in the presence of a current." Physcial Review Fluids. 2 (9), p. 094805. https://doi.org/10.1103/PhysRevFluids.2.094805

Adiabatic decay of internal solitons in a rotating ocean

Obregon, M. A., Raj, N. and Stepanyants, Y. A.. 2016. "Adiabatic decay of internal solitons in a rotating ocean." 20th Australasian Fluid Mechanics Conference (AFMC 2016). Perth, Australia 05 - 08 Dec 2016 Australia.

Modulational instability of wave trains in a rotating ocean

Nikitenkova, S. P., Singh, N. N. and Stepanyants, Y. A.. 2016. "Modulational instability of wave trains in a rotating ocean." 20th Australasian Fluid Mechanics Conference (AFMC 2016). Perth, Australia 05 - 08 Dec 2016 Australia.

Transformation of internal waves at the bottom ledge

Churaev, E. N., Semin, S. V. and Stepanyants, Y. A.. 2014. "Transformation of internal waves at the bottom ledge." 19th Australasian Fluid Mechanics Conference (AFMC 2014). Melbourne, Australia 08 - 11 Dec 2014 Australia.

Description of vortical flows of incompressible fluid in terms of quasi-potential function

Ermakov, A. M. and Stepanyants, Y. A.. 2016. "Description of vortical flows of incompressible fluid in terms of quasi-potential function." 20th Australasian Fluid Mechanics Conference (AFMC 2016). Perth, Australia 05 - 08 Dec 2016 Australia.

Interaction of solitons with long waves in a rotating fluid

Ostrovsky, L. A. and Stepanyants, Y. A.. 2016. "Interaction of solitons with long waves in a rotating fluid." Physica D: Nonlinear Phenomena. 333, pp. 266-275. https://doi.org/10.1016/j.physd.2016.02.008

Negative energy waves in shear flow with a linear profile

Maissa, Philippe, Rousseaux, Germain and Stepanyants, Yury. 2016. "Negative energy waves in shear flow with a linear profile." European Journal of Mechanics B: Fluids. 56, pp. 192-199. https://doi.org/10.1016/j.euromechflu.2016.01.003

Formation of wave packets in the Ostrovsky equation for both normal and anomalous dispersion

Grimshaw, Roger, Stepanyants, Yury and Alias, Azwani. 2016. "Formation of wave packets in the Ostrovsky equation for both normal and anomalous dispersion." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 472 (2185), pp. 1-20. https://doi.org/10.1098/rspa.2015.0416

Transformation of surface and internal waves on a bottom step

Kurkin, Andrey, Semin, Sergey and Stepanyants, Yury. 2015. "Transformation of surface and internal waves on a bottom step." Fundamental and Applied Hydrophysics (in Russian). 8 (3), pp. 3-19.

Modulational stability of weakly nonlinear wave-trains in media with small- and large-scale dispersions

Nikitenkova, S., Singh, N. and Stepanyants, Y.. 2015. "Modulational stability of weakly nonlinear wave-trains in media with small- and large-scale dispersions." Chaos: an interdisciplinary journal of nonlinear science. 25 (12), pp. 123113-1. https://doi.org/10.1063/1.4937362

Transient free surface flow past a two-dimensional flat stern

Ogilat, Osama and Stepanyants, Yury. 2015. "Transient free surface flow past a two-dimensional flat stern." Discontinuity, Nonlinearity and Complexity. 4 (3), pp. 353-369. https://doi.org/10.5890/DNC.2015.09.010

The Bernoulli integral for a certain class of non-stationary viscous vortical flows of incompressible fluid

Stepanyants, Y. A. and Yakubovich, E. I.. 2015. "The Bernoulli integral for a certain class of non-stationary viscous vortical flows of incompressible fluid." Studies in Applied Mathematics. 135 (3), pp. 295-309. https://doi.org/10.1111/sapm.12087

Transformation of waves over a bottom step

Kurkin, Andrey, Semin, Sergey and Stepanyants, Yury. 2015. Transformation of waves over a bottom step. Nizhny Novgorod (Russia). Nizhny Novgorod State Technical University.

Transformation of surface waves over a bottom step

Kurkin, A. A., Semin, S. V. and Stepanyants, Yu A.. 2015. "Transformation of surface waves over a bottom step." Russian Academy of Sciences, Izvestiya: Atmospheric and Oceanic Physics. 51 (2), pp. 214-223. https://doi.org/10.1134/S0001433815020097

Modeling of transformation of surface wave packets interacting with abrupt bottom change

Brovchenko, Igor, Maderich, Vladimir, Semin, Sergey, Stepanyants, Yury and Terletska, Kateryna. 2015. "Modeling of transformation of surface wave packets interacting with abrupt bottom change." Applied Hydromechanics. 17 (1), pp. 3-9.

Dynamics of two charged particles in a creeping flow

Hassan, H. K. and Stepanyants, Y. A.. 2015. "Dynamics of two charged particles in a creeping flow." Journal of Physical Mathematics. 6 (2). https://doi.org/10.4172/2090-0902.1000145

Beyond the KdV: post-explosion development

Ostrovsky, L., Pelinovsky, E., Shrira, V. and Stepanyants, Y.. 2015. "Beyond the KdV: post-explosion development." Chaos: an interdisciplinary journal of nonlinear science. 25 (9), pp. 1-13. https://doi.org/10.1063/1.4927448

Generalized Korteweg–de Vries equation for internal waves in two-layer fluid

Giniyatullin, A. R., Kurkin, A. A., Kurkina, O. E. and Stepanyants, Y. A.. 2014. "Generalized Korteweg–de Vries equation for internal waves in two-layer fluid." Fundamental and Applied Hydrophysics (in Russian). 7 (4), pp. 16-28.

Transformation of internal waves passing over a bottom step

Churaev, Egor N., Semin, Sergey V. and Stepanyants, Yuri A.. 2015. "Transformation of internal waves passing over a bottom step." Journal of Fluid Mechanics. 768, pp. R3-1. https://doi.org/10.1017/jfm.2015.92

Structure of internal solitary waves in two-layer fluid at near-critical situation

Kurkina, O., Singh, N. and Stepanyants, Y.. 2015. "Structure of internal solitary waves in two-layer fluid at near-critical situation." Communications in Nonlinear Science and Numerical Simulation. 22 (1-3), pp. 1235-1242. https://doi.org/10.1016/j.cnsns.2014.09.018

Dispersion properties of waves on a surface of viscous fluid covered by an elastic film

Averbukh, E. L., Kurkin, A. A., Stepanyants, Y. A. and Talipova, T. G.. 2014. "Dispersion properties of waves on a surface of viscous fluid covered by an elastic film." Fluid Dynamics. 49 (6), pp. 796-803. https://doi.org/10.1134/S0015462814060118

Transformation of narrowband wavetrains of surface gravity waves passing over a bottom step

Giniyatullin, A. R., Kurkin, A. A., Semin, S. V. and Stepanyants, Y. A.. 2014. "Transformation of narrowband wavetrains of surface gravity waves passing over a bottom step." Mathematical Modelling of Natural Phenomena (MMNP). 9 (5), pp. 73-82. https://doi.org/10.1051/mmnp/20149505

On stationary solutions of the reduced Gardner–Ostrovsky equation

Obregon, Maria and Stepanyants, Yury. 2014. "On stationary solutions of the reduced Gardner–Ostrovsky equation." Discontinuity, Nonlinearity and Complexity. 3 (4), pp. 445-456. https://doi.org/10.5890/DNC.2014.12.007

Nonlinear vector waves of a flexural mode in a chain model of atomic particles

Nikitenkova, S. P., Raj, N. and Stepanyants, Y. A.. 2015. "Nonlinear vector waves of a flexural mode in a chain model of atomic particles." Communications in Nonlinear Science and Numerical Simulation. 20 (3), pp. 731-742. https://doi.org/10.1016/j.cnsns.2014.05.031

Interaction of gaseous bubbles under the action of radiation modified Bjerknes force

Stepanyants, Yury and Yeoh, Guan. 2008. "Interaction of gaseous bubbles under the action of radiation modified Bjerknes force." 22nd International Congress of Theoretical and Applied Mechanics (IC-TAM2008). Adelaide, Australia 24 - 29 Aug 2008

Recent results on the problem of wave-current interaction including water depth, surface tension/amplitude and vorticity effects

Maissa, Philippe, Rousseaux, Germain and Stepanyants, Yury. 2013. "Recent results on the problem of wave-current interaction including water depth, surface tension/amplitude and vorticity effects." 7th International Conference on Coastal Dynamics. Arcachon, France 24 - 28 Jun 2013 Arcachon, France.

Nonlinear spectra of shallow water waves

Giovanangeli, J. -P., Kharif, C., Raj, N. and Stepanyants, Y.. 2013. "Nonlinear spectra of shallow water waves." Oceans - San Diego, 2013. San Diego, United States 23 - 26 Sep 2013 United States. IEEE (Institute of Electrical and Electronics Engineers). https://doi.org/10.23919/OCEANS.2013.6741132

Numerical study of nonlinear wave processes by means of discrete chain models

Obregon, M., Raj, N. and Stepanyants, Y.. 2012. "Numerical study of nonlinear wave processes by means of discrete chain models." Gu, Y. T. and Saha, Suvash C. (ed.) 4th International Conference on Computational Methods (ICCM 2012). Gold Coast, Australia 25 - 28 Nov 2012 Brisbane, Australia.

Stationary gravity waves with the zero mean vorticity in stratified fluid

Clamond, D. and Stepanyants, Y.. 2012. "Stationary gravity waves with the zero mean vorticity in stratified fluid." Studies in Applied Mathematics. 128 (1), pp. 59-85. https://doi.org/10.1111/j.1467-9590.2011.00530.x

Measuring rate of change of oxygen concentration and intrinsic oxidation rate in a pile of material

Bennett, John, Stepanyants, Yury and Ritchie, Ian. 2004. Measuring rate of change of oxygen concentration and intrinsic oxidation rate in a pile of material. WO 2004/072636 A1

Internal solitons in laboratory experiments: Comparison with theoretical models

Ostrovsky, L A. and Stepanyants, Y. A.. 2005. "Internal solitons in laboratory experiments: Comparison with theoretical models." Chaos: an interdisciplinary journal of nonlinear science. 15. https://doi.org/10.1063/1.2107087

Measurement of hydraulic conductivity using a radioactive or activatable tracer

Waring, Christopher Leslie, Airey, Peter Lewis and Stepanyants, Yury A.. 2007. Measurement of hydraulic conductivity using a radioactive or activatable tracer. AU2007231556

Measurement of hydraulic conductivity, porosity and lithology by neutron activation borehole logging at high spatial resolution increments

Waring, C. L., Stepanyants, Y. A., Hankin, S. I., Airey, P. L. and Peterson, M. A.. 2009. "Measurement of hydraulic conductivity, porosity and lithology by neutron activation borehole logging at high spatial resolution increments." Milne-Home, William A. (ed.) IAH Groundwater in The Sydney Basin Symposium (2009). Sydney, Australia 04 - 05 Aug 2009 Sydney, NSW, Australia.

Internal solitons in the ocean and their effect on underwater sound

Apel, John R., Ostrovsky, Lev A., Stepanyants, Yury A. and Lynch, James F.. 2007. "Internal solitons in the ocean and their effect on underwater sound." The Journal of the Acoustical Society of America. 121 (2), pp. 695-722. https://doi.org/10.1121/1.2395914

Influence of bottom boundary conditions for temperature on the heat distribution within oxidising heaps

Crawford, Jagoda and Stepanyants, Yury. 2005. "Influence of bottom boundary conditions for temperature on the heat distribution within oxidising heaps." Australian and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal. 46, pp. C1104-C1125.

Propagation of waves in shear flows

Fabrikant, Anatoly and Stepanyants, Yury. 1998. Propagation of waves in shear flows. Singapore. World Scientific Publishing.

Dispersion of long gravity-capillary surface waves and asymptotic equations for solitons

Stepanyants, Yury. 2005. "Dispersion of long gravity-capillary surface waves and asymptotic equations for solitons." Proceedings of the Russian Academy of Engineering Sciences Series: Applied Mathematics and Mechanics. 14, pp. 33-40.

Scalar description of three-dimensional vortex flows of incompressible fluid

Stepanyants, Yu. A. and Yakubovich, Evsey. 2011. "Scalar description of three-dimensional vortex flows of incompressible fluid." Doklady Physics. 56 (2), pp. 130-133. https://doi.org/10.1134/S1028335811020169

The inverse problem for the Gross-Pitaevskii equation

Malomed, Boris A. and Stepanyants, Yury A.. 2010. "The inverse problem for the Gross-Pitaevskii equation." Chaos: an interdisciplinary journal of nonlinear science. 20 (1). https://doi.org/10.1063/1.3367776

Dynamics of two charged particles in viscous fluid at small Reynolds numbers

Stepanyants, Y. A. and Strunin, D. V.. 2011. "Dynamics of two charged particles in viscous fluid at small Reynolds numbers." de Oliveira, Cassiano (ed.) 2011 International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Enginnering (MC 2011). Rio de Janeiro, Brazil 08 - 12 May 2011 Rio de Janeiro.

Nanoparticle dynamics in a viscous fluid at small Reynolds numbers

Stepanyants, Yury A. and Yeoh, Guan H.. 2010. "Nanoparticle dynamics in a viscous fluid at small Reynolds numbers." Teh, Kian, Davies, Ian and Howard, Ian (ed.) 6th Australasian Congress on Applied Mechanics (ACAM 6). Perth, Western Australia 12 - 15 Dec 2010 Perth, Australia.

Localised nonlinear optical modes and the corresponding support structures: exact solutions to the nonlinear Schrodinger equation with external potentials

Malomed, B. A. and Stepanyants, Y. A.. 2010. "Localised nonlinear optical modes and the corresponding support structures: exact solutions to the nonlinear Schrodinger equation with external potentials." ICEAA 2010: International Conference on Electromagnetics in Advanced Applications. Sydney, Australia 20 - 24 Sep 2010 Sydney, Australia. https://doi.org/10.1109/ICEAA.2010.5651681

Lump solutions of 2D generalized Gardner equation

Stepanyants, Y. A., Ten, I. K. and Tomita, H.. 2006. "Lump solutions of 2D generalized Gardner equation." Luo, Albert C. J., Dai, Liming and Hamidzadeh, Hamid R. (ed.) Conference on Nonlinear Science and Complexity (2006). Beijing, China 07 - 12 Aug 2006 Singapore.

Internal solitons in the ocean

Apel, John R., Ostrovsky, Lev A., Stepanyants, Yury A. and Lynch, James F.. 2006. Internal solitons in the ocean. Woods Hole, MA. United States. Woods Hole Oceanographic Institution.

Tsunami surge in a river: a hydraulic jump in an inhomogeneous channel

Caputo, Jean-Guy and Stepanyants, Y. A.. 2007. "Tsunami surge in a river: a hydraulic jump in an inhomogeneous channel." Kundu, Anjan (ed.) Tsunami and nonlinear waves. Berlin, Germany. Springer. pp. 97-112

Solutions classification to the extended reduced Ostrovsky equation

Stepanyants, Yury A.. 2008. "Solutions classification to the extended reduced Ostrovsky equation." Symmetry, Integrability and Geometry: Methods and Applications. 4. https://doi.org/10.3842/SIGMA.2008.073

Mechanisms of particle transport acceleration in porous media

Panfilov, M., Panfilova, I. and Stepanyants, Y.. 2008. "Mechanisms of particle transport acceleration in porous media." Transport in Porous Media. 74 (1), pp. 49-71. https://doi.org/10.1007/s11242-007-9201-9

Particle and bubble dynamics in a creeping flow

Stepanyants, Yury and Yeoh, Guan. 2009. "Particle and bubble dynamics in a creeping flow." European Journal of Mechanics B: Fluids. 28 (5), pp. 619-629. https://doi.org/10.1016/j.euromechflu.2009.04.004

On stationary solutions of the reduced Ostrovsky equation: periodic waves, compactons and compound solitons

Stepanyants, Yury. 2006. "On stationary solutions of the reduced Ostrovsky equation: periodic waves, compactons and compound solitons." Chaos, Solitons and Fractals. 28 (1), pp. 193-204. https://doi.org/10.1016/j.chaos.2005.05.020

The motion of a cylindrical body in a stratified fluid under the action of a radiation force

Kozyrev, O. R., Reznik, S. N. and Stepanyants, Yu. A.. 2009. "The motion of a cylindrical body in a stratified fluid under the action of a radiation force." Journal of Applied Mathematics and Mechanics. 73 (2), pp. 188-195. https://doi.org/10.1016/j.jappmathmech.2009.04.008

On numerical solution of the Gardner Ostrovsky equation

Download files

Published Version

1967

450

9

1

Export as

Related outputs