Interaction of plane solitons in the 2D Gardner equation

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena Pub Date : 2025-05-13 DOI:10.1016/j.physd.2025.134736

R. Fariello , Y.A. Stepanyants , T.G. Talipova

引用次数: 0

Abstract

The asymptotic approach is suggested for the description of stationary patterns formed by two plane solitons interacting at an angle to each other within the 2D Gardner equation that describes internal waves in oceans. The approach is applicable both to integrable and nonintegrable evolution equations possessing soliton solutions. An approximate set of equations describing soliton fronts in the x,y-plane is derived for symmetric soliton patterns and solved analytically for small-amplitude solitons and numerically for large-amplitude solitons. Spatial shifts of soliton fronts caused by the nonlinear interaction of solitons are obtained.

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二维Gardner方程中平面孤子的相互作用

在描述海洋内波的二维加德纳方程中，建议用渐近方法来描述由两个平面孤子以一定角度相互作用形成的固定模式。该方法适用于具有孤子解的可积和不可积演化方程。导出了对称孤子图中描述x，y平面上孤子锋面的近似方程组，并对小振幅孤子进行了解析求解，对大振幅孤子进行了数值求解。得到了由孤子非线性相互作用引起的孤子锋的空间位移。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Physica D: Nonlinear Phenomena 物理-物理：数学物理

CiteScore

7.30

自引率

7.50%

发文量

213

审稿时长

65 days

期刊介绍： Physica D (Nonlinear Phenomena) publishes research and review articles reporting on experimental and theoretical works, techniques and ideas that advance the understanding of nonlinear phenomena. Topics encompass wave motion in physical, chemical and biological systems; physical or biological phenomena governed by nonlinear field equations, including hydrodynamics and turbulence; pattern formation and cooperative phenomena; instability, bifurcations, chaos, and space-time disorder; integrable/Hamiltonian systems; asymptotic analysis and, more generally, mathematical methods for nonlinear systems.