两种新型双分量广义复短脉冲方程的达布变换

IF 1 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Reports on Mathematical Physics Pub Date : 2022-10-01 DOI:10.1016/S0034-4877(22)00063-5

Xinyue Li, Zhixin Zhang, Qiulan Zhao , Chuanzhong Li

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引用次数: 2

摘要

短脉冲方程能够描述超短脉冲，它在光纤传输领域中起着至关重要的作用。本文研究了一类广义复短脉冲方程及其双分量推广。首先证明它们是Lax可积的。然后分别通过矢状变换得到它们新的Lax对进行达布变换。对于广义复短脉冲方程，我们给出了不同的Darboux矩阵，并验证了其可行性，然后利用广义Darboux变换重点讨论了高阶半有理孤子解。对于耦合广义复短脉冲方程，通过选择不同的种子解，应用达布变换讨论精确解。

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Darboux transformation of two novel two-component generalized complex short pulse equations

The short pulse equation is able to describe ultra short pulse, which plays a crucial part in the field of optical fiber propagation. In this paper, we investigate a generalized complex short pulse equation and its two-component generalization. We first prove that they are Lax integrable. Subsequently, we obtain their new Lax pairs through hodograph transformation to carry out Darboux transformation, respectively. For the generalized complex short pulse equation, we provide a different Darboux matrix and verify that it is feasible, then we focus on higher-order semi-rational soliton solutions by means of generalized Darboux transformation. For the coupled generalized complex short pulse equations, we apply Darboux transformation to discuss exact solutions by choosing different seed solutions.

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来源期刊

Reports on Mathematical Physics 物理-物理：数学物理

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： Reports on Mathematical Physics publish papers in theoretical physics which present a rigorous mathematical approach to problems of quantum and classical mechanics and field theories, relativity and gravitation, statistical physics, thermodynamics, mathematical foundations of physical theories, etc. Preferred are papers using modern methods of functional analysis, probability theory, differential geometry, algebra and mathematical logic. Papers without direct connection with physics will not be accepted. Manuscripts should be concise, but possibly complete in presentation and discussion, to be comprehensible not only for mathematicians, but also for mathematically oriented theoretical physicists. All papers should describe original work and be written in English.