复短脉冲方程的广义达布变换及高阶孤子解

数学物理学报 ›› 2026, Vol. 46 ›› Issue (6): 2167-2182.

复短脉冲方程的广义达布变换及高阶孤子解

何凤蝶(), 苗园园^*(), 毛辉()

南宁师范大学数学与统计学院南宁 530100

收稿日期:2025-07-21 修回日期:2026-03-24 出版日期:2026-12-26 发布日期:2026-08-14
通讯作者: 苗园园 E-mail:18776194852@163.com;15903006513@163.com;maohuimath@163.com
作者简介:何凤蝶, E-mail: 18776194852@163.com;
毛辉, E-mail: maohuimath@163.com
基金资助:
国家自然科学基金项目(12261061)

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

Fengdie He(), Yuanyuan Miao^*(), Hui Mao()

School of Mathematics and Statistics, Nanning Normal University, Nanning 530100

Received:2025-07-21 Revised:2026-03-24 Online:2026-12-26 Published:2026-08-14
Contact: Yuanyuan Miao E-mail:18776194852@163.com;15903006513@163.com;maohuimath@163.com
Supported by:
NSFC(12261061)

摘要/Abstract

摘要：

该文首先通过互反变换将复短脉冲 (CSP) 方程转化为连带 CSP 方程, 推导出 CSP 方程的 $N$ 重达布变换的行列式表示, 进而构造 CSP 方程的广义达布变换. 作为应用, 利用广义达布变换给出了 CSP 方程在零种子解情况下的高阶孤子解, 通过具体实例, 对一些高阶孤子解的动力学行为进行图解分析, 揭示了smooth 孤子解、cuspon 孤子解和 loop 孤子解的非线性相互作用特征.

关键词: 复短脉冲方程, 互反变换, 广义达布变换, 高阶孤子解

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

中图分类号:

O175.24

何凤蝶, 苗园园, 毛辉. 复短脉冲方程的广义达布变换及高阶孤子解[J]. 数学物理学报, 2026, 46(6): 2167-2182.

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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