J 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 FREIRE

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

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:

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

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.
Displayed: 24/12/2024 03:59