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

被引：12
|
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
收藏
页码：181 / 235
页数：55
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