LEAL DA SILVA, Priscila and Igor LEITE FREIRE. Integrability, existence of global solutions, and wave breaking criteria for a generalization of the Camassa-Holm equation. Studies in Applied Mathematics. Hoboken (USA): WILEY, 2020, vol. 145, No 3, p. 537-562. ISSN 0022-2526. Available from: https://dx.doi.org/10.1111/sapm.12327.
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Basic 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
Original language English
Type of outcome Article in a journal
Field of Study 10101 Pure mathematics
Country of publisher United States of America
Confidentiality degree is not subject to a state or trade secret
WWW Studies in Applied Mathematics
RIV identification code RIV/47813059:19610/20:A0000083
Organization unit Mathematical Institute in Opava
Doi http://dx.doi.org/10.1111/sapm.12327
UT WoS 000550818600001
Keywords in English Camassa-Holm equation; global well-posedness; integrability; wave breaking
Tags MÚ
Tags International impact, Reviewed
Changed by Changed by: Mgr. Aleš Ryšavý, učo 28000. Changed: 6/4/2021 07:14.
Abstract
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.
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