周期性无穷隙函数类中带有附加项的正弦-戈登方程积分法

IF 0.5 Q3 MATHEMATICS

Russian Mathematics Pub Date : 2024-06-25 DOI:10.3103/s1066369x24700191

A. B. Khasanov, Kh. N. Normurodov

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引用次数: 0

摘要

摘要本文使用反谱问题方法对周期性无穷间隙函数类中带有附加项的非线性正弦-戈登类型方程进行积分。证明了三次连续可微周期性无限间隙函数类中杜布罗文微分方程无限系统的考奇问题的可解性。证明了通过求解杜布罗文方程组和第一迹公式构造的均匀收敛函数序列的和满足一个带附加项的正弦-戈登式方程。

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Integration of a Sine-Gordon Type Equation with an Additional Term in the Class of Periodic Infinite-Gap Functions

Abstract

In this paper, the inverse spectral problem method is used to integrate a nonlinear sine-Gordon type equation with an additional term in the class of periodic infinite-gap functions. The solvability of the Cauchy problem for an infinite system of Dubrovin differential equations in the class of three times continuously differentiable periodic infinite-gap functions is proved. It is shown that the sum of a uniformly convergent functional series constructed by solving the Dubrovin system of equations and the first trace formula satisfies a sine-Gordon type equation with an additional term.

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来源期刊

Russian Mathematics MATHEMATICS-

CiteScore

0.90

自引率

25.00%

发文量

期刊介绍： Russian Mathematics is a peer reviewed periodical that encompasses the most significant research in both pure and applied mathematics.