Orbital stability of the sum of N peakons for the generalized higher-order Camassa-Holm equation

被引：2

作者：

Deng, Tongjie ^{[1
]}

Chen, Aiyong ^{[2
]}

机构：

[1] Hunan Normal Univ, Sch Math & Stat, Key Lab Comp & Stochast Math, Minist Educ, Changsha 410081, Hunan, Peoples R China

[2] Hunan First Normal Univ, Dept Math, Changsha 410205, Hunan, Peoples R China

来源：

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK | 2022年 / 73卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Generalized higher-order Camassa-Holm equation; Peakons; Multi-peakons; Orbital stability; SHALLOW-WATER EQUATION; BREAKING; WAVES;

D O I：

10.1007/s00033-022-01796-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The orbital stability of peakons for the generalized higher-order Camassa-Holm equation has been established by Qin et al. (Z Angew Math Phys 73:96, 2022. https://doi.org/10.1007/s00033-022-01739-3) . In this paper, using energy argument and combining the method of the orbital stability of a single peakon with monotonicity of the local energy norm, we prove that the sum of N sufficiently decoupled peakons is orbitally stable in the energy space.

引用

页数：28

共 19 条

[1] A general family of multi-peakon equations and their properties [J].

Anco, Stephen C. ;

Recio, Elena .

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2019, 52 (12)

[2]

[Anonymous], 1998, Ann. Scuola Norm. Sup. Pisa Cl. Sci

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

CAMASSA, R ;

HOLM, DD .

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

[4] Stability of peakons and periodic peakons for a nonlinear quartic Camassa-Holm equation [J].

Chen, Aiyong ;

Deng, Tongjie ;

Qiao, Zhijun .

MONATSHEFTE FUR MATHEMATIK, 2022, 198 (02) :251-288

[5] Stability of the Camassa-Holm peakons in the dynamics of a shallow-water-type system [J].

Chen, Robin Ming ;

Liu, Xiaochuan ;

Liu, Yue ;

Qu, Changzheng .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2016, 55 (02)

[6]

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

[7] Wave breaking for nonlinear nonlocal shallow water equations [J].

Constantin, A ;

Escher, J .

ACTA MATHEMATICA, 1998, 181 (02) :229-243

[8] Orbital stability of solitary waves for a shallow water equation [J].

Constantin, A ;

Molinet, L .

PHYSICA D, 2001, 157 (1-2) :75-89

[9] Existence of permanent and breaking waves for a shallow water equation: A geometric approach [J].

Constantin, A .

ANNALES DE L INSTITUT FOURIER, 2000, 50 (02) :321-+

[10] Stability of multipeakons [J].

El Dika, Khaled ;

Molinet, Luc .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2009, 26 (04) :1517-1532

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