Cauchy problem for the nonlinear Hirota equation in the class of periodic infinite-zone functions

IF 0.7 4区数学 Q2 MATHEMATICS

St Petersburg Mathematical Journal Pub Date : 2023-11-09 DOI:10.1090/spmj/1780

G. Mannonov, A. Khasanov

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引用次数: 0

Abstract

In this paper, the method of inverse spectral problem is used to integrate the nonlinear Hirota equation in the class of periodic infinite-zone functions. An evolution of the spectral data of the periodic Dirac operator is introduced, where the coefficient of this operator is the solution of the nonlinear Hirota equation. The solvability of the Cauchy problem for an infinite system of Dubrovin differential equations in the class of five times continuously differentiable periodic infinite-zone functions is shown. In addition, it is proved that if the initial function is a π \pi -periodic real-analytic function, then the solution of the Cauchy problem for the Hirota equation is also a real-analytic function in the variable x x ; and if the number π / 2 \pi /2 is a period (antiperiod) of the initial function, then the number π / 2 \pi /2 is a period (antiperiod) in the variable x x of the solution of the Cauchy problems for the Hirota equation.

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周期无穷区函数中非线性Hirota方程的Cauchy问题

本文利用谱逆问题的方法对一类周期无穷区函数中的非线性Hirota方程进行积分。介绍了周期狄拉克算子谱数据的演化，其中该算子的系数是非线性Hirota方程的解。给出了一类五次连续可微周期无穷带函数的Dubrovin微分方程无穷系的Cauchy问题的可解性。此外，证明了如果初始函数是π \ π -周期实解析函数，则Hirota方程的Cauchy问题的解也是变量x x上的实解析函数;如果数π /2 \pi /2是初始函数的一个周期(反周期)，那么数π /2 \pi /2就是变量x x的一个周期(反周期)，这是Hirota方程的柯西问题的解。

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

St Petersburg Mathematical Journal MATHEMATICS-

CiteScore

1.00

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： This journal is a cover-to-cover translation into English of Algebra i Analiz, published six times a year by the mathematics section of the Russian Academy of Sciences.