Spectral analysis and long-time asymptotics for the potential Wadati-Konno-Ichikawa equation

被引：11

作者：

Chen, Mingming ^{[1
]}

Geng, Xianguo ^{[1
]}

Wang, Kedong ^{[1
]}

机构：

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

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2021年 / 501卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Nonlinear steepest descent method; Long-time asymptotics; Potential Wadati-Konno-Ichikawa equation; STEEPEST DESCENT METHOD; NONLINEAR SCHRODINGER-EQUATION; INVERSE SCATTERING;

D O I：

10.1016/j.jmaa.2021.125170

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The long-time asymptotics of the solution of the initial value problem for the potential Wadati-Konno-Ichikawa (pWKI) equation are obtained by using the nonlinear steepest descent method. Based on the spectral analysis and inverse scattering methods, we first construct a basic Riemann-Hilbert problem related to the solution of the pWKI equation. Various Deift-Zhou contour deformations and the motivation behind them are given. Through several proper transformations between the corresponding Riemann-Hilbert problems and strict error estimates, the leading-order asymptotics of the solution of the initial value problem for the pWKI equation is finally obtained. (c) 2021 Elsevier Inc. All rights reserved.

引用

页数：27

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