Scholarlink

Abstract <p> In this paper the inverse spectral problem method is applied to integrate a nonlinearHirota-type equation with a self-consistent series source in the class of periodic infinite-gapfunctions. An infinite system of differential equations is derived that describes the evolution ofspectral data for the periodic Dirac operator. The solvability of the Cauchy problem for thissystem in the class of six-times continuously differentiable periodic infinite-gap functions is proved.In addition, an algorithm for finding infinite-gap solution to the Cauchy problem for a Hirota-typeequation with a self-consistent series source is proposed, and an exact solution is found in the caseof the single-gap case for the Dirac operator.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

The Cauchy Problem for a Nonlinear Hirota-Type Equation with a Self-Consistent Series Source

  • 期刊论文

  • 发表日期：

    2025年10月1日

查看全文
  • A. B. Khasanov,
  • R. Kh. Eshbekov

摘要

Abstract

In this paper the inverse spectral problem method is applied to integrate a nonlinearHirota-type equation with a self-consistent series source in the class of periodic infinite-gapfunctions. An infinite system of differential equations is derived that describes the evolution ofspectral data for the periodic Dirac operator. The solvability of the Cauchy problem for thissystem in the class of six-times continuously differentiable periodic infinite-gap functions is proved.In addition, an algorithm for finding infinite-gap solution to the Cauchy problem for a Hirota-typeequation with a self-consistent series source is proposed, and an exact solution is found in the caseof the single-gap case for the Dirac operator.