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Symmetric interactions of plane solitons in two-dimensional nonlinear lattices

Communications in Nonlinear Science and Numerical Simulation, ISSN: 1007-5704, Vol: 114, Page: 106602
2022
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Findings on Nonlinear Science and Numerical Simulation Detailed by Investigators at University of Southern Queensland (Symmetric Interactions of Plane Solitons In Two-dimensional Nonlinear Lattices)

2022 NOV 04 (NewsRx) -- By a News Reporter-Staff News Editor at Math Daily News -- Research findings on Mathematics - Nonlinear Science and Numerical

Article Description

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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