Long time behavior and soliton solution for the Harry Dym equation

被引：11
作者：
Xiao, Yu [1 ]
Fan, Engui [2 ]
机构：
[1] Henan Agr Univ, Coll Informat & Management Sci, Zhengzhou 450046, Henan, Peoples R China
[2] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2019年 / 480卷 / 01期
基金：
美国国家科学基金会;
关键词：
Harry Dym equation; Riemann-Hilbert problem; Long time asymptotic behavior; Soliton solution; CAMASSA-HOLM EQUATION; ASYMPTOTICS; DYM; HARRY;
D O I：
10.1016/j.jmaa.2019.06.019
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we consider the Harry-Dym equation with the decaying initial data. Using the nonlinear steepest decent method of Deift and Zhou for Riemann-Hilbert problems, we firstly obtain the explicit leading asymptotic of solution of by Harry-Dym equation by transforming its Lax pairs. What'more, in the framework of the Riemann-Hilbert problem, we can find cusp soliton. (C) 2019 Published by Elsevier Inc.
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页数：29
相关论文
共 20 条
[1]  
Boutet de Monvel A., 2007, Math. Sci. Res. Inst. Publ., V55, P53
[2]  
de Monvel AB, 2008, CONTEMP MATH, V458, P99
[3]   Riemann-Hilbert approach for the Camassa-Holm equation on the line [J].
de Monvel, Anne Boutet ;
Shepelsky, Dmitry .
COMPTES RENDUS MATHEMATIQUE, 2006, 343 (10) :627-632
[4]   The short-wave model for the Camassa-Holm equation: a Riemann-Hilbert approach [J].
de Monvel, Anne Boutet ;
Shepelsky, Dmitry ;
Zielinski, Lech .
INVERSE PROBLEMS, 2011, 27 (10)
[5]   LONG-TIME ASYMPTOTICS FOR THE CAMASSA-HOLM EQUATION [J].
De Monvel, Anne Boutet ;
Kostenko, Aleksey ;
Shepelsky, Dmitry ;
Teschl, Gerald .
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2009, 41 (04) :1559-1588
[6]   A STEEPEST DESCENT METHOD FOR OSCILLATORY RIEMANN-HILBERT PROBLEMS - ASYMPTOTICS FOR THE MKDV EQUATION [J].
DEIFT, P ;
ZHOU, X .
ANNALS OF MATHEMATICS, 1993, 137 (02) :295-368
[7]   N-LOOP SOLITONS AND THEIR LINK WITH THE COMPLEX HARRY-DYM EQUATION [J].
DMITRIEVA, LA .
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1994, 27 (24) :8197-8205
[8]  
Gesztesy F., 1992, Rep. Math. Phys, V31, P113, DOI [10.1016/0034-4877(92)90008-o, DOI 10.1016/0034-4877(92)90008-O]
[9]   Long-Time Asymptotics for the Korteweg-de Vries Equation via Nonlinear Steepest Descent [J].
Grunert, Katrin ;
Teschl, Gerald .
MATHEMATICAL PHYSICS ANALYSIS AND GEOMETRY, 2009, 12 (03) :287-324
[10]   DERIVATION AND IMPLICIT SOLUTION OF THE DYM,HARRY, EQUATION AND ITS CONNECTIONS WITH THE KORTEWEG-DEVRIES EQUATION [J].
HEREMAN, W ;
BANERJEE, PP ;
CHATTERJEE, MR .
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1989, 22 (03) :241-255
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