一类新的广义r- s无色散Harry Dym方程解的大t行为

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters Pub Date : 2025-09-19 DOI:10.1016/j.aml.2025.109768

Linlin Gui, Yufeng Zhang

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引用次数: 0

摘要

Manakov和Santini等人解决了无色散可积偏微分方程的逆散射问题，并利用这些问题构造了可积方程的形式化解。本文从一对二维矢量场中导出了一个新的方程，称为广义无r-次色散Harry Dym （g-rdDym）方程，该方程可简化为标准（2+1）维无r-次色散Harry Dym （rdDym）方程。然后利用相关的Riemann-Hilbert （RH）逆问题构造了Cauchy问题形式解的大t行为，并利用指数函数描述了一类新的特解。本文不仅研究了rdDym方程，还研究了与之相对应的广义方程g-rdDym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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The large t behaviour of solutions for a new generalized r-th dispersionless Harry Dym equation

Manakov and Santini, etc., have solved inverse scattering problem for dispersionless integrable partial differential equations (PDEs), and used these to construct the formal solutions for integrable equations. In this paper, we derive a new equation from a pair of two-dimensional vector fields, termed the generalized r-th dispersionless Harry Dym (g-rdDym) equation, which reduces to the standard (2+1)-dimensional r-th dispersionless Harry Dym (rdDym) equation. Then we construct large

t

behaviour of formal solution of Cauchy problem by applying associated Riemann-Hilbert (RH) inverse problem, and describe a new class of particular solutions via the exponential functions. This paper investigates not only the rdDym equation, but also its corresponding generalized equation, i.e. the g-rdDym equation.

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来源期刊

Applied Mathematics Letters 数学-应用数学

CiteScore

7.70

自引率

5.40%

发文量

347

审稿时长

10 days

期刊介绍： The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.