Spectral analysis and long-time asymptotics for the Harry Dym-type equation with the Schwartz initial data

被引：13

作者：

Liu, Wenhao ^{[1
]}

Geng, Xianguo ^{[1
]}

Wang, Kedong ^{[1
]}

Chen, Mingming ^{[1
]}

机构：

[1] Zhengzhou Univ, Sch Math & Stat, 100 Kexue Rd, Zhengzhou 450001, Henan, Peoples R China

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2023年 / 357卷

基金：

中国国家自然科学基金;

关键词：

Riemann-Hilbert problem; Harry Dym-type equation; Nonlinear steepest decent method; Long-time asymptotics; STEEPEST DESCENT METHOD; ALGEBRO-GEOMETRIC SOLUTIONS; CAMASSA-HOLM EQUATION;

D O I：

10.1016/j.jde.2023.02.001

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the Cauchy problem of the Harry Dym-type equation associated with the 3 x 3 matrix spectral problem by establishing the corresponding Riemann-Hilbert problem with the initial value lies in Schwartz space. Based on the nonlinear steepest descent method, we give the detailed contour deformation process to reduce the basic Riemann-Hilbert problem to a model Riemann-Hilbert problem, by which the long-time asymptotics for the Harry Dym-type equation is obtained with the aid of a series of precise and uniform error estimates. (c) 2023 Elsevier Inc. All rights reserved.

引用

页码：181 / 235

页数：55

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