Integrable reduction and solitons of the Fokas–Lenells equation

IF 1.4 4区数学 Q2 MATHEMATICS, APPLIED

IMA Journal of Applied Mathematics 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

IMA Journal of Applied Mathematics 数学-应用数学

CiteScore

2.30

自引率

8.30%

发文量

审稿时长

24 months

期刊介绍： The IMA Journal of Applied Mathematics is a direct successor of the Journal of the Institute of Mathematics and its Applications which was started in 1965. It is an interdisciplinary journal that publishes research on mathematics arising in the physical sciences and engineering as well as suitable articles in the life sciences, social sciences, and finance. Submissions should address interesting and challenging mathematical problems arising in applications. A good balance between the development of the application(s) and the analysis is expected. Papers that either use established methods to address solved problems or that present analysis in the absence of applications will not be considered. The journal welcomes submissions in many research areas. Examples are: continuum mechanics materials science and elasticity, including boundary layer theory, combustion, complex flows and soft matter, electrohydrodynamics and magnetohydrodynamics, geophysical flows, granular flows, interfacial and free surface flows, vortex dynamics; elasticity theory; linear and nonlinear wave propagation, nonlinear optics and photonics; inverse problems; applied dynamical systems and nonlinear systems; mathematical physics; stochastic differential equations and stochastic dynamics; network science; industrial applications.