Breather solutions and higher-order rogue wave solutions to the modified complex short pulse equation

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters Pub Date : 2025-06-25 DOI:10.1016/j.aml.2025.109664

Cong Lv , Deqin Qiu , Yongshuai Zhang

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引用次数: 0

Abstract

Breather solutions and higher-order rogue wave solutions with two arbitrary parameters

a

and

c

of the modified complex short pulse (mcSP) equation are generated based on the reciprocal transformation and the Darboux transformation. We construct the

n

th-order Darboux transformation in terms of determinants whose entries are represented by initial eigenfunctions and seed solutions. Furthermore, the formulae for the higher-order rogue wave solutions of the mcSP equation are obtained by using the Taylor expansion with the help of degenerate eigenvalues

λ_{j} \to a^{2} c - \frac{i a \sqrt{1 - 4 a^{2} c^{2}}}{2}, j = 1, 2, \dots, n

. The analyticity of first-order rogue wave solution is studied. Some figures illustrate dynamic structures of the rogue waves from the first to the third order. The effect of the choice of parameters on the rogue waves are specifically discussed.

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修正复短脉冲方程的呼吸解和高阶异常波解

基于倒易变换和达布变换，得到了修正复短脉冲方程的呼吸解和具有任意参数a和c的高阶异常波解。我们用行列式来构造n阶达布变换，行列式的项由初始特征函数和种子解表示。此外，利用退化特征值λj→a2c−ia1−4a2c22，j=1,2，…，n，利用泰勒展开式得到了mcSP方程的高阶异常波解的表达式。研究了一阶异常波解的解析性。一些图表说明了从一阶到三阶的异常浪的动力结构。具体讨论了参数选择对异常波的影响。

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

Applied Mathematics Letters 数学-应用数学

CiteScore

7.70

自引率

5.40%

发文量

347

审稿时长

10 days

期刊介绍： The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.