Cauchy Problem for the Nonlinear Liouville Equation in the Class of Periodic Infinite-Gap Functions

IF 0.8 4区数学 Q2 MATHEMATICS

Differential Equations Pub Date : 2023-11-23 DOI:10.1134/s00122661230100087

A. B. Khasanov, Kh. N. Normurodov, U. O. Khudayorov

引用次数: 0

Abstract

The inverse spectral problem method is used to integrate the nonlinear Liouville equation in the class of periodic infinite-gap functions. The evolution of the spectral data of the periodic Dirac operator whose coefficient is a solution of the nonlinear Liouville equation is introduced. 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 function series constructed by solving the Dubrovin system of equations and using the first trace formula satisfies the Liouville equation.

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一类周期无限间隙函数中非线性Liouville方程的Cauchy问题

摘要利用逆谱问题方法对一类周期无限间隙函数中的非线性Liouville方程进行积分。介绍了系数为非线性Liouville方程解的周期性dirac算子谱数据的演化过程。证明了一类三次连续可微周期无限间隙函数的无限Dubrovin微分方程组的Cauchy问题的可解性。通过求解杜布罗文方程组，利用第一迹公式构造的一致收敛函数级数的和满足Liouville方程。

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

Differential Equations 数学-数学

CiteScore

1.30

自引率

33.30%

发文量

审稿时长

3-8 weeks

期刊介绍： Differential Equations is a journal devoted to differential equations and the associated integral equations. The journal publishes original articles by authors from all countries and accepts manuscripts in English and Russian. The topics of the journal cover ordinary differential equations, partial differential equations, spectral theory of differential operators, integral and integral–differential equations, difference equations and their applications in control theory, mathematical modeling, shell theory, informatics, and oscillation theory. The journal is published in collaboration with the Department of Mathematics and the Division of Nanotechnologies and Information Technologies of the Russian Academy of Sciences and the Institute of Mathematics of the National Academy of Sciences of Belarus.