N-fold Darboux transformation and exact solutions for the nonlocal Fokas–Lenells equation on the vanishing and plane wave backgrounds

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-04-25 DOI:10.1515/ijnsns-2021-0224

Li Li, Yiyan Liu, Fajun Yu

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引用次数: 0

Abstract

Abstract In this paper, we propose and investigate the reverse-space–time nonlocal nonlinear Fokas–Lenells equation by the idea of Ablowitz and Musslimani. The reverse-space–time Fokas–Lenells equation, associated with a 2 × 2 matrix Lax pair, is the important integrable system, which can be reduced to the nonlocal Fokas–Lenells equation. Based on its Lax pair, we construct nonlocal version of N-fold Darboux transformation (DT) for the Fokas–Lenells equation, and obtain two kinds of soliton solutions from vanishing and plane wave backgrounds. Further some novel one-soliton and two-soliton are derived with the zero and nonzero seed solutions through complex computations, including the bright soliton, kink soliton and breather wave soliton. Moreover, various graphical analyses on the presented solutions are made to reveal the dynamic behaviors, which display the elastic interactions between two solitons and their amplitudes keeping unchanged after the interactions except for the phase shifts. It is clearly shown that these solutions have new properties which differ from ones of the classical Fokas–Lenells equation.

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消失波和平面波背景下非局部Fokas-Lenells方程的n倍Darboux变换和精确解

摘要本文利用Ablowitz和Musslimani的思想，提出并研究了逆时空非局部非线性Fokas-Lenells方程。与2 × 2矩阵Lax对相关的逆时空Fokas-Lenells方程是重要的可积系统，它可以简化为非局域Fokas-Lenells方程。基于它的Lax对，构造了Fokas-Lenells方程的n重Darboux变换(DT)的非局部版本，得到了消失波和平面波背景下的两种孤子解。在此基础上，通过复杂的计算，导出了具有零和非零种子解的新型单孤子和双孤子，包括明亮孤子、扭结孤子和呼吸波孤子。此外，对所提出的解进行了各种图形分析，揭示了两个孤子之间的动力学行为，这些动力学行为显示了两个孤子之间的弹性相互作用，并且相互作用后它们的振幅除了相移外保持不变。结果表明，这些解具有不同于经典Fokas-Lenells方程的新性质。

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.