用Gel’fand - levitan - marchenko方程求解负阶非线性波动方程的逆散射方法

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

Theoretical and Mathematical Physics Pub Date : 2025-01-27 DOI:10.1134/S0040577925010039

M. I. Ismailov, C. Sabaz

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引用次数: 0

摘要

利用一阶三方程线性系统的Lax层次，得到了一类负阶ablowitz - kap - newell - segur非线性演化方程。当线性系统成为具有实反对称势和实对称势的经典Zakharov-Shabat系统时，研究了直线上的逆散射问题。在此基础上，利用Gel’fand - levitan - marchenko方程的逆散射方法，得到了耦合标量场的非线性Klein-Gordon方程的积分-微分版和负阶修正Korteweg-de Vries方程的\(N\) -孤子解。

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Inverse scattering method via the Gel’fand–Levitan–Marchenko equation for some negative-order nonlinear wave equations

A class of negative-order Ablowitz–Kaup–Newell–Segur nonlinear evolution equations are obtained by applying the Lax hierarchy of a first-order linear system of three equations. The inverse scattering problem on the line is examined in the cases where the linear system becomes the classical Zakharov–Shabat system with real antisymmetric and real symmetric potentials. Referring to these results, the \(N\)-soliton solutions for the integro-differential version of the nonlinear Klein–Gordon equation coupled to a scalar field and the negative-order modified Korteweg-de Vries equation are obtained by using the inverse scattering method via the Gel’fand–Levitan–Marchenko 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.