多分量离散复杂短脉冲方程的环解、逆解和孤子解

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

Theoretical and Mathematical Physics Pub Date : 2025-02-25 DOI:10.1134/S0040577925020047

A. Inam, M. ul Hassan

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引用次数: 0

摘要

利用Lax对表示和Darboux变换，给出了多分量离散复短脉冲方程的可积离散化方法。通过将\(2\times2\) Lax矩阵推广到\(2^L\times2^L\) Lax矩阵，利用分块矩阵探讨了Lax对的表示。研究了矩阵解上的DT，并利用拟行列式的性质生成了多分量dCSP方程的解。通过展开拟行列式，我们证明了孤子解可以用普通行列式的比值来表示。在此基础上，利用适当的连续极限得到了连续复短脉冲方程的多孤子解。

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Loop, cuspon, and soliton solutions of a multicomponent discrete complex short-pulse equation

We present an integrable discretization of a multicomponent discrete complex short-pulse (dCSP) equation in terms of a Lax pair representation and a Darboux transformation (DT). The Lax pair representation is explored using block matrices by extending the \(2\times2\) Lax matrices to \(2^L\times2^L\) Lax matrices. The DT on the matrix solutions is studied and is used to generate solutions of the multicomponent dCSP equation by using the properties of quasideterminants. By expanding the quasideterminants, we then show the soliton solutions to be expressed as ratios of ordinary determinants. Further, an appropriate continuum limit is applied to obtain multisoliton solutions of the continuous complex short-pulse equation.

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来源期刊

Theoretical and Mathematical Physics 物理-物理：数学物理

CiteScore

1.60

自引率

20.00%

发文量

103

审稿时长

4-8 weeks

期刊介绍： Theoretical and Mathematical Physics covers quantum field theory and theory of elementary particles, fundamental problems of nuclear physics, many-body problems and statistical physics, nonrelativistic quantum mechanics, and basic problems of gravitation theory. Articles report on current developments in theoretical physics as well as related mathematical problems. Theoretical and Mathematical Physics is published in collaboration with the Steklov Mathematical Institute of the Russian Academy of Sciences.