On the Hirota equation with a self-consistent source

IF 1 4区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL Theoretical and Mathematical Physics Pub Date : 2024-11-26 DOI:10.1134/S0040577924110059
A. B. Khasanov, A. A. Reyimberganov
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Abstract

We develop the formalism of the inverse scattering problem method for the Cauchy problem for the defocusing Hirota equation with a self-consistent source. The specific feature of the considered Cauchy problem is that the solution is assumed to approach nonzero limits as the spatial variable approaches the plus and minus infinities. The purpose of the paper is to present two main steps of the formalism: first, the inverse problem for the associated linear Zakharov–Shabat system and, second, the evolution of the associated scattering data. A theorem is proved on the evolution of scattering data of a self-adjoint Zakharov–Shabat system, with the potential given by a solution of the defocusing Hirota equation with a self-consistent source.

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关于具有自洽源的广田方程
我们针对具有自洽源的广达(Hirota)离焦方程的考奇问题,提出了反散射问题法的形式主义。所考虑的 Cauchy 问题的具体特征是,当空间变量接近正无穷大和负无穷大时,假设解接近非零极限。本文旨在介绍形式主义的两个主要步骤:第一,相关线性 Zakharov-Shabat 系统的逆问题;第二,相关散射数据的演化。本文证明了一个关于自共轭 Zakharov-Shabat 系统散射数据演化的定理,该系统的势由具有自洽源的离焦 Hirota 方程的解给出。
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
Theoretical and Mathematical Physics
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.
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