广义耦合导数非线性薛定谔方程的孤子分子、孤子共振以及 breather-positon 解

Abstract

Abstract:

In this paper, we focus on the general coupled derivative nonlinear Schrödinger equation which is distinguished by the nonlinear self-steepening of narrow pulses. Based on the Lax pair, the $N$-fold Darboux transformation in the form of determinants. Subsequently, using the Darboux transformation and limiting techniques, we can systematically study the soliton molecules, solitons resonances and breather positons for the general coupled derivative nonlinear Schrödinger equation. By choosing the zero seed solutions, different types of $N$-soliton molecules and the soliton resonances with soliton molecules and the dark soliton/breather-like soliton are obtained. Then by choosing the nonzero seed solutions, the higher-order breather positons can be derived. It is noteworthy that the central region of breather positons manifests rogue waves, thus prompting the proposal that they may elucidate the underlying mechanism of rogue wave generation. The approach shown in this paper to gain the soliton interaction solutions and breather positons can contribute to the research field of physical phenomena.

Key words: the general coupled derivative nonlinear Schr?dinger equation, Darboux transformation, soliton molecules, soliton resonances, breather positon

CLC Number:

O175.29

Pingping Zeng, Pingan Zeng, Guoan Xu. Soliton Molecules, Soliton Resonances and Breather Positon Solutions for the General Coupled Derivative Nonlinear Schrödinger Equation[J].Acta mathematica scientia,Series A, 2026, 46(6): 2183-2195.

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References 46

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Soliton Molecules, Soliton Resonances and Breather Positon Solutions for the General Coupled Derivative Nonlinear Schrödinger Equation

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