Integration of the sine-Gordon equation with a source and an additional term

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)00067-2

Umid Azadovich Hoitmetov

引用次数: 0

Abstract

The work is devoted to solving the Cauchy problem for the sine-Gordon equation with an additional term and a self-consistent source in the class of rapidly decreasing functions. The problem is solved by the inverse scattering method. Several special cases of the sine-Gordon equation with an additional term are given, which can be integrated using the inverse scattering method, for example, the loaded sine-Gordon equation. Several examples are given to illustrate the application of the obtained results.

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带源项和附加项的正弦戈登方程的积分

本文研究了一类速降函数中带附加项和自洽源的正弦-戈登方程的柯西问题。采用逆散射法解决了该问题。给出了几种可以用逆散射法积分的带有附加项的正弦-戈登方程的特殊情况，如加载正弦-戈登方程。给出了几个例子来说明所得结果的应用。

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

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.