复短脉冲方程的广义达布变换及高阶孤子解

Abstract

Abstract:

This paper begins by transforming the complex short pulse (CSP) equation into an associated CSP equation through a reciprocal transformation, and subsequently derives the determinant representation of the $N$-fold Darboux transformation for the CSP equation, thereby constructing its generalized Darboux transformation. As an application, the generalized Darboux transformation is employed to derive high order soliton solutions for the CSP equation under the zero seed solution. Through concrete examples, the dynamical behaviors of certain high order soliton solutions are graphically analyzed, revealing the nonlinear interaction characteristics of smooth soliton solutions, cuspon soliton solutions, and loop soliton solutions.

Key words: complex short pulse equation, generalized Darboux transformation, high order soliton solutions

CLC Number:

O175.24

Fengdie He, Yuanyuan Miao, Hui Mao. Generalized Darboux Transformation and High Order Soliton Solutions of the Complex Short Pulse Equation[J].Acta mathematica scientia,Series A, 2026, 46(6): 2167-2182.

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Generalized Darboux Transformation and High Order Soliton Solutions of the Complex Short Pulse Equation

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