Complex Dynamics of Solitons in Rotating Fluids

Ostrovsky, Lev A. and Stepanyants, Yury A. ORCID: https://orcid.org/0000-0003-4546-0310 (2022) Complex Dynamics of Solitons in Rotating Fluids. In: Mathematical Methods in Modern Complexity Science. Nonlinear Systems and Complexity (33). Springer Nature, Switzerland, pp. 63-78. ISBN 9783030794118


Abstract

We outline the dynamics of solitons interacting with each other and with a long-wave background. It is shown that the asymptotic procedure reduces the initial nonintegrable PDE to the system of homogeneous ODEs with variable coefficients describing the amplitudes and trajectories of solitons as radiating particles. The resulting motion is due to the interplay of different factors: interaction between solitons, which affect each other by their 'tails', dissipation due to radiation of each soliton, and energy exchange with the long background wave. In many cases, it is often possible to distinguish these processes by their time scales. The final stage of interaction is always a nontrivial equilibrium; in particular, for two solitons the amplitudes tend to the same value, whereas their positions on the background wave remain different so that the solitons remain interacting with each other even asymptotically. A field for further development of the model is outlined.


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Item Type: Book Chapter (Commonwealth Reporting Category B)
Refereed: Yes
Item Status: Live Archive
Additional Information: Files associated with this item cannot be displayed due to copyright restrictions.
Faculty/School / Institute/Centre: Current – Faculty of Health, Engineering and Sciences - School of Mathematics, Physics and Computing (1 Jan 2022 -)
Faculty/School / Institute/Centre: Current - Institute for Advanced Engineering and Space Sciences - Centre for Astrophysics (1 Aug 2018 -)
Date Deposited: 21 Apr 2022 01:43
Last Modified: 21 Apr 2022 01:43
Uncontrolled Keywords: Solitons; dynamical system; asymptotic method; soliton interaction with long wave; comples dynamics
Fields of Research (2020): 37 EARTH SCIENCES > 3708 Oceanography > 370803 Physical oceanography
51 PHYSICAL SCIENCES > 5103 Classical physics > 510399 Classical physics not elsewhere classified
49 MATHEMATICAL SCIENCES > 4901 Applied mathematics > 490105 Dynamical systems in applications
Socio-Economic Objectives (2020): 28 EXPANDING KNOWLEDGE > 2801 Expanding knowledge > 280118 Expanding knowledge in the mathematical sciences
28 EXPANDING KNOWLEDGE > 2801 Expanding knowledge > 280120 Expanding knowledge in the physical sciences
Identification Number or DOI: https://doi.org/10.1007/978-3-030-79412-5
URI: http://eprints.usq.edu.au/id/eprint/47574

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