The short pulse equation by a Riemann-Hilbert approach

被引：59

作者：

de Monvel, Anne Boutet ^{[1
]}

Shepelsky, Dmitry ^{[2
]}

Zielinski, Lech ^{[3
]}

机构：

[1] Univ Paris Diderot, Inst Math Jussieu PRG, 8 Pl Aurelie Nemours,Bat Sophie Germain,Case 7012, F-75205 Paris 13, France

[2] Inst Low Temp Phys, Div Math, 47 Lenin Ave, UA-61103 Kharkov, Ukraine

[3] Univ Littoral Cote dOpale, LMPA, 50 Rue F Buisson,CS 80699, F-62228 Calais, France

来源：

LETTERS IN MATHEMATICAL PHYSICS | 2017年 / 107卷 / 07期

关键词：

Short pulse equation; Short wave equation; Camassa-Holm-type equation; Inverse scattering transform; Riemann-Hilbert problem; CAMASSA-HOLM EQUATION; STEEPEST DESCENT METHOD; SOLITARY-WAVE SOLUTIONS; LONG-TIME ASYMPTOTICS; INVERSE SCATTERING; NONLINEAR MEDIA; WELL-POSEDNESS; BEHAVIOR; SOLITONS; LINE;

D O I：

10.1007/s11005-017-0945-z

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We develop a Riemann-Hilbert approach to the inverse scattering transform method for the short pulse (SP) equation with zero boundary conditions (as ). This approach is directly applied to a Lax pair for the SP equation. It allows us to give a parametric representation of the solution to the Cauchy problem. This representation is then used for studying the longtime behavior of the solution as well as for retrieving the soliton solutions. Finally, the analysis of the longtime behavior allows us to formulate, in spectral terms, a sufficient condition for the wave breaking.

引用

页码：1345 / 1373

页数：29

共 36 条

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