Integrable reduction and solitons of the Fokas–Lenells equation

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-06-01 DOI:10.1093/imamat/hxab020

Theodoros P Horikis

引用次数: 1

Abstract

Novel soliton structures are constructed for the Fokas–Lenells equation. In so doing, and after discussing the stability of continuous waves, a multiple scales based perturbation theory is used to reduce the equation to a Korteweg–de Vries system whose single soliton solution gives rise to intricate (and rather unexpected) solutions to the original system. Both the focusing and defocusing equations are considered and it is found that dark solitons may exist in both cases while in the focusing case antidark solitons are also possible. These findings are quite surprising as the relative nonlinear Schrödinger equation does not exhibit these solutions. So far, similar abundance of solutions has only been observed in relative coupled systems.

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Fokas–Lenells方程的可积约化和孤立子

为Fokas–Lenells方程构造了新的孤子结构。在这样做的过程中，在讨论了连续波的稳定性之后，使用基于多尺度的微扰理论将方程简化为Korteweg–de Vries系统，该系统的单孤立子解会对原始系统产生复杂（而且相当出乎意料）的解。考虑了聚焦和散焦方程，发现在这两种情况下都可能存在暗孤子，而在聚焦情况下也可能存在反暗孤子。这些发现非常令人惊讶，因为相对非线性的薛定谔方程没有表现出这些解。到目前为止，只有在相对耦合的系统中才观察到类似的大量解。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.