Well-posedness, travelling waves and geometrical aspects of generalizations of the Camassa-Holm equation
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F19%3AA0000061" target="_blank" >RIV/47813059:19610/19:A0000061 - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S0022039619302505?via%3Dihub" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0022039619302505?via%3Dihub</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jde.2019.05.033" target="_blank" >10.1016/j.jde.2019.05.033</a>
Alternative languages
Result language
angličtina
Original language name
Well-posedness, travelling waves and geometrical aspects of generalizations of the Camassa-Holm equation
Original language description
In this paper we consider a five-parameter equation including the Camassa-Holm and the Dullin-Gottwald-Holm equations, among others. We prove the existence and uniqueness of solutions of the Cauchy problem using Kato's approach. Conservation laws of the equation, up to second order, are also investigated. From these conservation laws we establish some properties for the solutions of the equation and we also find a quadrature for it. The quadrature obtained is of capital importance in a classification of bounded travelling wave solutions. We also find some explicit solutions, given in terms of elliptic integrals. Finally, we classify the members of the equation describing pseudo-spherical surfaces.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Differential Equations
ISSN
0022-0396
e-ISSN
1090-2732
Volume of the periodical
267
Issue of the periodical within the volume
9
Country of publishing house
US - UNITED STATES
Number of pages
52
Pages from-to
5318-5369
UT code for WoS article
000480416600011
EID of the result in the Scopus database
2-s2.0-85066321295