A Riemann-Hilbert approach to the modified Camassa-Holm equation with step-like boundary conditions

被引：3

作者：

Karpenko, Iryna ^{[1
,2
]}

Shepelsky, Dmitry ^{[1
]}

Teschl, Gerald ^{[2
]}

机构：

[1] B Verkin Inst Low Temp Phys & Engn, 47 Nauky Ave, UA-61103 Kharkiv, Ukraine

[2] Univ Vienna, Fac Math, Oskar Morgenstern Pl 1, A-1090 Vienna, Austria

来源：

MONATSHEFTE FUR MATHEMATIK | 2023年 / 201卷 / 01期

关键词：

Riemann-Hilbert problem; Camassa-Holm equation; LONG-TIME ASYMPTOTICS; NONLINEAR SCHRODINGER-EQUATION; KORTEWEG-DE-VRIES; SHALLOW-WATER EQUATION; CAUCHY-PROBLEM; BLOW-UP; INVERSE SCATTERING; COUPLING PROBLEM; WEAK SOLUTIONS; PEAKONS;

D O I：

10.1007/s00605-022-01786-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The paper aims at developing the Riemann-Hilbert (RH) approach for the modified Camassa-Holm (mCH) equation on the line with non-zero boundary conditions, in the case when the solution is assumed to approach two different constants at different sides of the line. We present detailed properties of spectral functions associated with the initial data for the Cauchy problem for the mCH equation and obtain a representation for the solution of this problem in terms of the solution of an associated RH problem.

引用

页码：127 / 172

页数：46

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