Kinematics of interacting solitons in two-dimensional space

Article

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
Article Title

Kinematics of interacting solitons in two-dimensional space

Article CategoryArticle
AuthorsOstrovsky, L.A. (Author) and Stepanyants, Y. A. (Author)
Journal TitleRussian Journal of Earth Science
Journal Citation20, pp. 1-11
Article NumberES4007
Number of Pages11
Year2020
Place of PublicationRussia
Digital Object Identifier (DOI)https://doi.org/10.2205/2020ES000735
Web Address (URL)http://rjes.wdcb.ru/doi/2020ES000735-res.html
Abstract

A simple kinematic approach to the description of the interaction between solitons is developed. It is applicable to both integrable and non-integrable two-dimensional models, including those commonly used for studying the surface and internal oceanic waves. This approach allows obtaining some important characteristics of the interaction between solitary waves propagating at an angle to each other. The developed theory is validated by comparison with the exact solutions of the Kadomtsev-Petviashvili equation and then applied to the observed interaction of solitary internal waves in a two-layer fluid within the two-dimensional Benjamin-Ono model.

KeywordsSurface and internal waves; solitons; kinematic approach; Kadomtsev-Petviashvili equation; Benjamin-Ono equation; two-soliton solutions
Contains Sensitive ContentDoes not contain sensitive content
ANZSRC Field of Research 2020401207. Fundamental and theoretical fluid dynamics
370803. Physical oceanography
490109. Theoretical and applied mechanics
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File reproduced in accordance with the copyright policy of the publisher/author.

Institution of OriginUniversity of Southern Queensland
Byline AffiliationsUniversity of Colorado Boulder, United States
School of Sciences
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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.
On numerical solution of the Gardner Ostrovsky equation
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
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
Front solutions of Richards' equation
Caputo, Jean-Guy and Stepanyants, Yury. 2008. "Front solutions of Richards' equation." Transport in Porous Media. 74 (1), pp. 1-20. https://doi.org/10.1007/s11242-007-9180-x
Burgers-Rott vortices with surface tension
Stepanyants, Yury A. and Yeoh, Guan H.. 2008. "Burgers-Rott vortices with surface tension." Zeitschrift fuer Angewandte Mathematik und Physik. 59 (6), pp. 1057-1068. https://doi.org/10.1007/s00033-008-7071-9
Stationary bathtub vortices and a critical regime of liquid discharge
Stepanyants, Yury and Yeoh, Guan. 2008. "Stationary bathtub vortices and a critical regime of liquid discharge." Journal of Fluid Mechanics. 604 (1), pp. 77-98. https://doi.org/10.1017/S0022112008001080
Modelling internal solitary waves on the Australian North West Shelf
Grimshaw, Roger, Pelinovsky, Efim, Stepanyants, Yury and Talipova, Tatiana. 2006. "Modelling internal solitary waves on the Australian North West Shelf." Marine and Freshwater Research. 57 (3), pp. 265-272. https://doi.org/10.1071/MF05016