Stability of traveling wave solutions for the second-order Camassa-Holm equation

被引：0

作者：

Ding, Danping ^{[1
]}

Li, Yun ^{[1
]}

机构：

[1] Jiangsu Univ, Sch Math Sci, Xuefu Rd, Zhenjiang 212013, Jiangsu, Peoples R China

来源：

MONATSHEFTE FUR MATHEMATIK | 2023年 / 202卷 / 04期

关键词：

Second-order Camassa-Holm equation; Travelling wave solution; Orbital stability; Pseudo-conformal transformation; Smoothing; ORBITAL STABILITY; DIFFEOMORPHISM GROUP; PEAKONS; SOLITONS;

D O I：

10.1007/s00605-023-01828-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper studies the stability of traveling wave solutions of the second-order Camassa-Holm equation. Applying the pseudo-conformal transformation, the solutions near the travelling wave solutions of the second-order C-H equation are decomposed: lambda(1/2) (t) u (t, y + x (t)) = eta (t, y) + Q (y) .The uniform boundedness of the difference term is proved by smoothing technique, and the orbital stability of the traveling wave solution of the second-order C-H equation is obtained.

引用

页码：713 / 740

页数：28

共 24 条

[1] AN INTEGRABLE SHALLOW-WATER EQUATION WITH PEAKED SOLITONS [J].

CAMASSA, R ;

HOLM, DD .

PHYSICAL REVIEW LETTERS, 1993, 71 (11) :1661-1664

[2]

Chen A., 2021, MONATSH MATH, P1

[3] Well-posedness of higher-order Camassa-Holm equations [J].

Coclite, G. M. ;

Holden, H. ;

Kadsen, K. H. .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2009, 246 (03) :929-963

[4]

Constantin A, 2000, COMMUN PUR APPL MATH, V53, P603

[5] Integrability of invariant metrics on the diffeomorphism group of the circle [J].

Constantin, A ;

Kolev, B .

JOURNAL OF NONLINEAR SCIENCE, 2006, 16 (02) :109-122

[6] Geodesic flow on the diffeomorphism group of the circle [J].

Constantin, A ;

Kolev, B .

COMMENTARII MATHEMATICI HELVETICI, 2003, 78 (04) :787-804

[7] Blow-up solution near the traveling waves for the second-order Camassa-Holm equation [J].

Ding, Danping ;

Wang, Kai .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2021, 58

[8] Decay property of solutions near the traveling wave solutions for the second-order Camassa-Holm equation [J].

Ding, Danping ;

Wang, Kai .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2019, 183 :230-258

[9] Lipschitz metric for the periodic second-order Camassa Holm equation [J].

Ding, Danping ;

Zhang, Shuanghua .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2017, 451 (02) :990-1025

[10] Traveling solutions and evolution properties of the higher order Camassa-Holm equation [J].

Ding, Danping .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2017, 152 :1-11

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