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@article{49380,
author = {Leal da Silva, Priscila and Leite Freire, Igor},
article_location = {Hoboken (USA)},
article_number = {3},
doi = {http://dx.doi.org/10.1111/sapm.12327},
keywords = {Camassa-Holm equation; global well-posedness; integrability; wave breaking},
language = {eng},
issn = {0022-2526},
journal = {Studies in Applied Mathematics},
title = {Integrability, existence of global solutions, and wave breaking criteria for a generalization of the Camassa-Holm equation},
url = {https://onlinelibrary.wiley.com/doi/10.1111/sapm.12327},
volume = {145},
year = {2020}
}
TY - JOUR
ID - 49380
AU - Leal da Silva, Priscila - Leite Freire, Igor
PY - 2020
TI - Integrability, existence of global solutions, and wave breaking criteria for a generalization of the Camassa-Holm equation
JF - Studies in Applied Mathematics
VL - 145
IS - 3
SP - 537-562
EP - 537-562
PB - WILEY
SN - 00222526
KW - Camassa-Holm equation
KW - global well-posedness
KW - integrability
KW - wave breaking
UR - https://onlinelibrary.wiley.com/doi/10.1111/sapm.12327
N2 - 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.
ER -
LEAL DA SILVA, Priscila a Igor LEITE FREIRE. Integrability, existence of global solutions, and wave breaking criteria for a generalization of the Camassa-Holm equation. \textit{Studies in Applied Mathematics}. Hoboken (USA): WILEY, 2020, roč.~145, č.~3, s.~537-562. ISSN~0022-2526. Dostupné z: https://dx.doi.org/10.1111/sapm.12327.
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