Highly localized horseshoe ripplons and solitons in positive dispersion media

Article

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

Article Title	Highly localized horseshoe ripplons and solitons in positive dispersion media
ERA Journal ID	1302
Article Category	Article
Authors	Zhang, Zhao, Guo, Qi and Stepanyants, Yury
Journal Title	Wave Motion
Journal Citation	128
Article Number	103326
Number of Pages	13
Year	2024
Publisher	Elsevier
Place of Publication	Netherlands
ISSN	0165-2125
Digital Object Identifier (DOI)	https://doi.org/10.1016/j.wavemoti.2024.103326
Web Address (URL)	https://www.sciencedirect.com/science/article/pii/S0165212524000568
Abstract	In this study, we systematically review various ripplon solutions to the Kadomtsev–Petviashvili equation with positive dispersion (KP1 equation). We show that there are mappings that allow one to transform the horseshoe solitons and curved lump chains of the KP1 equation into circular solitons of the cylindrical Korteweg–de Vries (cKdV) equation and two-dimensional solitons of the cylindrical Kadomtsev–Petviashvili (cKP) equation. Then, we present analytical solutions that describe new nonlinear highly localized ripplons of a horseshoe shape. Ripplons are two-dimensional waves with an oscillatory structure in space and a decaying character in time; they are similar to lumps but non-stationary. In the limiting case, the horseshoe ripplons reduce to solitons decaying with time and having bent fronts. Such entities can play an important role in the description of strong turbulence in plasma and other media.
Keywords	Decaying solutions; Kadomtsev–Petviashvili equation; Ripplons; Lumps
Contains Sensitive Content	Does not contain sensitive content
ANZSRC Field of Research 2020	490199. Applied mathematics not elsewhere classified
Byline Affiliations	South China Normal University, China
	School of Mathematics, Physics and Computing

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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.

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