Detailed Information on Publication Record
2020
Integrability, existence of global solutions, and wave breaking criteria for a generalization of the Camassa-Holm equation
LEAL DA SILVA, Priscila and Igor LEITE FREIREBasic information
Original name
Integrability, existence of global solutions, and wave breaking criteria for a generalization of the Camassa-Holm equation
Authors
LEAL DA SILVA, Priscila (76 Brazil) and Igor LEITE FREIRE (76 Brazil, guarantor, belonging to the institution)
Edition
Studies in Applied Mathematics, Hoboken (USA), WILEY, 2020, 0022-2526
Other information
Language
English
Type of outcome
Článek v odborném periodiku
Field of Study
10101 Pure mathematics
Country of publisher
United States of America
Confidentiality degree
není předmětem státního či obchodního tajemství
References:
RIV identification code
RIV/47813059:19610/20:A0000083
Organization unit
Mathematical Institute in Opava
UT WoS
000550818600001
Keywords in English
Camassa-Holm equation; global well-posedness; integrability; wave breaking
Tags
Tags
International impact, Reviewed
Změněno: 6/4/2021 07:14, Mgr. Aleš Ryšavý
Abstract
V originále
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.