CLASSICAL SOLUTIONS OF THE GENERALIZED CAMASSA-HOLM EQUATION

被引：0

作者：

Holmes, John ^{[1
]}

Thompson, Ryan C. ^{[2
]}

机构：

[1] Ohio State Univ, Dept Math, 231 W 18th Ave, Columbus, OH 43210 USA

[2] Univ North Georgia, Dept Math, Dahlonega, GA 30597 USA

来源：

ADVANCES IN DIFFERENTIAL EQUATIONS | 2017年 / 22卷 / 5-6期

关键词：

SHALLOW-WATER EQUATION; WAVES;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, well-posedness in C-1(R) (a.k.a. classical solutions) for a generalized Camassa-Holm. equation (g-kbCH) having (k+1)-degree nonlinearities is shown. This result holds for the Camassa-Holm, the Degasperis-Procesi and the Novikov equations, which improves upon earlier results in Sobolev and Besov spaces.

引用

页码：339 / 362

页数：24

共 19 条

[1] SUR LA GEOMETRIE DIFFERENTIELLE DES GROUPES DE LIE DE DIMENSION INFINIE ET SES APPLICATIONS A LHYDRODYNAMIQUE DES FLUIDES PARFAITS [J].

ARNOLD, V .

ANNALES DE L INSTITUT FOURIER, 1966, 16 (01) :319-&

[2] Global conservative solutions of the Camassa-Holm equation [J].

Bressan, Alberto ;

Constantin, Adrian .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2007, 183 (02) :215-239

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

CAMASSA, R ;

HOLM, DD .

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

[4]

Chen RM, 2013, MATH ANN, V357, P1245, DOI 10.1007/s00208-013-0939-9

[5] 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-+

[6] The Hydrodynamical Relevance of the Camassa-Holm and Degasperis-Procesi Equations [J].

Constantin, Adrian ;

Lannes, David .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2009, 192 (01) :165-186

[7]

Degasperis A., 1999, Symmetry and perturbation theory, P23

[8] GROUPS OF DIFFEOMORPHISMS AND MOTION OF AN INCOMPRESSIBLE FLUID [J].

EBIN, DG ;

MARSDEN, J .

ANNALS OF MATHEMATICS, 1970, 92 (01) :102-&

[9] SYMPLECTIC STRUCTURES, THEIR BACKLUND-TRANSFORMATIONS AND HEREDITARY SYMMETRIES [J].

FUCHSSTEINER, B ;

FOKAS, AS .

PHYSICA D, 1981, 4 (01) :47-66

[10]

Grayshan K., 2013, Adv. Dyn. Syst. Appl, V8, P217

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