General rogue wave solutions and their dynamics in the complex modified Korteweg–de Vries equation

IF 4.6 2区物理与天体物理 Q2 MATERIALS SCIENCE, MULTIDISCIPLINARY Results in Physics Pub Date : 2025-03-03 DOI:10.1016/j.rinp.2025.108174

Yan Zhu , Lijuan Qin , Zhiqiang Yang , Zhenting Chen , Zhenyun Qin , Gui Mu

引用次数: 0

Abstract

By means of the Hirota bilinear method together with the Kadomtsev–Petviashvili hierarchy reduction technique, general higher-order rogue wave solutions of the complex modified Korteweg–de Vries equation are derived explicitly. These solutions are expressed succinctly in terms of Gram determinants whose matrix elements are Schur polynomials. It is found that the highest peak amplitude of

N

th-order rogue waves turns out to be

2 N + 1

times its background amplitude. The

N

th-order rogue wave solutions contain the

N - 1

irreducible complex parameters. By selecting different values of these free parameters, the rich dynamic behaviors of rogue wave solutions of the complex modified Korteweg–de Vries equation are discovered.

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复杂修正Korteweg-de Vries方程中一般异常波解及其动力学

利用Hirota双线性方法和Kadomtsev-Petviashvili层次约简技术，明确地导出了复修正Korteweg-de Vries方程的一般高阶异动波解。这些解被简洁地表示为矩阵元素为舒尔多项式的克行列式。结果表明，n阶异常波的峰值幅值为其背景幅值的2N+1倍。N阶异常波解包含N−1个不可约复参数。通过选取这些自由参数的不同值，发现了复杂修正Korteweg-de Vries方程异常波解的丰富动力特性。

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

Results in Physics MATERIALS SCIENCE, MULTIDISCIPLINARYPHYSIC-PHYSICS, MULTIDISCIPLINARY

CiteScore

8.70

自引率

9.40%

发文量

754

审稿时长

50 days

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