The complex MKDV equation with step-like initial data: Large time asymptotic analysis

被引：1

作者：

Wang, Zhaoyu

Xu, Kai

Fan, Engui ^{[1
]}

机构：

[1] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China

来源：

JOURNAL OF MATHEMATICAL PHYSICS | 2023年 / 64卷 / 10期

基金：

中国国家自然科学基金;

关键词：

NONLINEAR SCHRODINGER-EQUATION; WAVE PROPAGATION; MICROPOLAR MEDIA; KDV; BEHAVIOR;

D O I：

10.1063/5.0131306

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

In this paper, we study large-time asymptotics for the complex modified Korteveg-de Vries equation with step-like initial data. It is shown that the step-like initial problem can be described by a matrix Riemann-Hilbert problem. Further we apply the steepest descent method to obtain different large-time asymptotics in the Zakharov-Manakov region, a plane wave region, and a slow decay region.

引用

页数：19

共 50 条

[1] Long-time behavior of the solution to the mKdV equation with step-like initial data
Minakov, Alexander
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2011, 44 (08)
[2] On a Riemann-Hilbert problem for the focusing nonlocal mKdV equation with step-like initial data
Liu, Leilei
Zhang, Weiguo
APPLIED MATHEMATICS LETTERS, 2021, 116
[3] Long-time Asymptotic for the Derivative Nonlinear Schrodinger Equation with Step-like Initial Value
Xu, Jian
Fan, Engui
Chen, Yong
MATHEMATICAL PHYSICS ANALYSIS AND GEOMETRY, 2013, 16 (03) : 253 - 288
[4] ON THE LONG-TIME ASYMPTOTIC BEHAVIOR OF THE MODIFIED KORTEWEG-DE VRIES EQUATION WITH STEP-LIKE INITIAL DATA
Grava, Tamara
Minakov, Alexander
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2020, 52 (06) : 5892 - 5993
[5] Focusing NLS Equation: Long-Time Dynamics of Step-Like Initial Data
de Monvel, Anne Boutet
Kotlyarov, Vladimir P.
Shepelsky, Dmitry
INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2011, 2011 (07) : 1613 - 1653
[6] Long-time Asymptotic for the Derivative Nonlinear Schrödinger Equation with Step-like Initial Value
Jian Xu
Engui Fan
Yong Chen
Mathematical Physics, Analysis and Geometry, 2013, 16 : 253 - 288
[7] SOLUTIONS OF THE KORTEWEG-DEVRIES EQUATION WITH STEP-LIKE INITIAL DATA
KAPPELER, T
JOURNAL OF DIFFERENTIAL EQUATIONS, 1986, 63 (03) : 306 - 331
[8] Riemann-Hilbert problem and soliton solutions with their asymptotic analysis for the focusing nonlocal Hirota equation with step-like initial data
Lei, Ling
Tian, Shou-Fu
Zhang, Xiao-Fan
PHYSICA D-NONLINEAR PHENOMENA, 2024, 470
[9] Long-time asymptotics for the nonlocal nonlinear Schrodinger equation with step-like initial data
Rybalko, Yan
Shepelsky, Dmitry
JOURNAL OF DIFFERENTIAL EQUATIONS, 2021, 270 : 694 - 724
[10] Long-time asymptotics for the Korteweg-de Vries equation with step-like initial data
Egorova, Iryna
Gladka, Zoya
Kotlyarov, Volodymyr
Teschl, Gerald
NONLINEARITY, 2013, 26 (07) : 1839 - 1864

← 1 2 3 4 5 →