复合修正科特韦格-德-弗里斯方程中周期背景上的多重孤子和呼吸器

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters Pub Date : 2024-09-12 DOI:10.1016/j.aml.2024.109308

Jiguang Rao , Dumitru Mihalache , Jingsong He

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引用次数: 0

摘要

本研究探讨了复杂修正 Korteweg-de Vries 方程中周期背景上的多重孤子和呼吸解。通过双线性方法为这些解提供了紧凑的行列式公式及其详细的推导过程。我们证实，在周期性背景上，孤子振幅表现出规则的周期行为，而呼吸子振幅则表现出准周期行为，这是一个周期的呼吸子在另一个周期的周期波上传播时所预期的。本文提供了孤子和呼吸子的渐近表达式，以揭示周期背景下的孤子和呼吸子动力学，从而确定了推导解的高精确度。

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Multiple solitons and breathers on periodic backgrounds in the complex modified Korteweg–de Vries equation

This study explores multiple soliton and breather solutions on periodic backgrounds in the complex modified Korteweg–de Vries equation. The compact determinant formulas and their detailed derivation process for these solutions are provided via the bilinear method. We confirm that on periodic backgrounds, soliton amplitudes exhibit regular periodic behaviors, while breather amplitudes display quasi-periodic behaviors, as is expected for a breather with one period propagating over a periodic wave with another period. The asymptotic expressions for the solitons and breathers, which establish the high accuracy of the derived solutions, are provided to reveal the soliton and breather dynamics on the periodic backgrounds.

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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.