Integrability, existence of global solutions, and wave breaking criteria for a generalization 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%2F20%3AA0000083" target="_blank" >RIV/47813059:19610/20:A0000083 - isvavai.cz</a>
Result on the web
<a href="https://onlinelibrary.wiley.com/doi/10.1111/sapm.12327" target="_blank" >https://onlinelibrary.wiley.com/doi/10.1111/sapm.12327</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1111/sapm.12327" target="_blank" >10.1111/sapm.12327</a>
Alternative languages
Result language
angličtina
Original language name
Integrability, existence of global solutions, and wave breaking criteria for a generalization of the Camassa-Holm equation
Original language description
Recent generalizations of the Camassa-Holm equation are studied from the point of view of existence of global solutions, criteria for wave breaking phenomena and integrability. We provide conditions, based on lower bounds for the first spatial derivative of local solutions, for global well-posedness in Sobolev spaces for the family under consideration. Moreover, we prove that wave breaking phenomena occurs under certain mild hypothesis. Based on the machinery developed by Dubrovin [Commun. Math. Phys. 267, 117-139 (2006)] regarding bi-Hamiltonian deformations, we introduce the notion of quasi-integrability and prove that there exists a unique bi-Hamiltonian structure for the equation only when it is reduced to the Dullin-Gotwald-Holm equation. Our results suggest that a recent shallow water model incorporating Coriollis effects is integrable only in specific situations. Finally, to finish the scheme of geometric integrability of the family of equations initiated in a previous work, we prove that the Dullin-Gotwald-Holm equation describes 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
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Studies in Applied Mathematics
ISSN
0022-2526
e-ISSN
1467-9590
Volume of the periodical
145
Issue of the periodical within the volume
3
Country of publishing house
US - UNITED STATES
Number of pages
26
Pages from-to
537-562
UT code for WoS article
000550818600001
EID of the result in the Scopus database
2-s2.0-85088384561