Symmetric interactions of plane solitons in two-dimensional nonlinear lattices

Nikitenkova, Svetlana and Stepanyants, Yury ORCID: https://orcid.org/0000-0003-4546-0310 (2022) Symmetric interactions of plane solitons in two-dimensional nonlinear lattices. Communications in Nonlinear Science and Numerical Simulation, 114:106602. pp. 1-10. ISSN 1007-5704


Abstract

We apply the asymptotic approach for the description of two plane solitons interacting under an angle to each other in 2D Toda lattices with the quadratic or triangle/hexagonal structure. We demonstrate the influence of lattice anisotropy on dispersion relations and soliton structures. With the help of the asymptotic approach, we study soliton interactions in the long-wave approximation and show that it is possible to find the spatial phase shifts experienced by each soliton due to the interaction with its counterpart. In contrast to earlier studied soliton interactions within the quasi-one-dimensional equations, here we consider a fully two-dimensional arrangement with an arbitrary angle between soliton fronts.


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Item Type: Article (Commonwealth Reporting Category C)
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 – Faculty of Health, Engineering and Sciences - School of Mathematics, Physics and Computing (1 Jan 2022 -)
Date Deposited: 13 Jun 2022 03:34
Last Modified: 13 Jun 2022 03:34
Uncontrolled Keywords: Toda lattice; Quadratic lattice; Triangle/hexagonal lattice; Soliton; Nonlinear interaction; Asymptotic method
Fields of Research (2020): 49 MATHEMATICAL SCIENCES > 4901 Applied mathematics > 490109 Theoretical and applied mechanics
51 PHYSICAL SCIENCES > 5103 Classical physics > 510399 Classical physics not elsewhere classified
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/10.1016/j.cnsns.2022.106602
URI: http://eprints.usq.edu.au/id/eprint/48953

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