Integration of the Korteweg–de Vries Equation with Time-Dependent Coefficients in the Case of Moving Eigenvalues of the Sturm–Liouville Operator

IF 0.5 Q3 MATHEMATICS

Russian Mathematics Pub Date : 2024-08-15 DOI:10.3103/s1066369x2470035x

U. A. Hoitmetov, T. G. Khasanov

引用次数: 0

Abstract

The inverse scattering method is used to integrate the Korteweg–de Vries equation with time-dependent coefficients. We derive the evolution of the scattering data of the Sturm–Liouville operator whose coefficient is a solution of the Korteweg–de Vries equation with time-dependent coefficients. An algorithm for constructing exact solutions of the Korteweg–de Vries equation with time-dependent coefficients is also proposed; we reduce it to the inverse problem of scattering theory for the Sturm–Liouville operator. Examples illustrating the stated algorithm are given.

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在 Sturm-Liouville 算子特征值移动的情况下，对带有时变系数的 Korteweg-de Vries 方程进行积分

摘要使用反向散射法来积分系数随时间变化的 Korteweg-de Vries 方程。我们推导了Sturm-Liouville算子的散射数据的演变，该算子的系数是Korteweg-de Vries方程随时间变化系数的解。我们还提出了一种算法，用于构建系数随时间变化的 Korteweg-de Vries 方程的精确解；我们将其简化为 Sturm-Liouville 算子的散射理论逆问题。我们给出了说明所述算法的示例。

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

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.