Integrability, existence of global solutions, and wave breaking criteria for a generalization of the Camassa-Holm equation

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Integrability, existence of global solutions, and wave breaking criteria for a generalization of the Camassa-Holm equation

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Integrability, existence of global solutions, and wave breaking criteria for a generalization of the Camassa-Holm equation

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2020

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Studies in Applied Mathematics

ISSN

0022-2526

e-ISSN

1467-9590

Svazek periodika

145

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

26

Strana od-do

537-562

Kód UT WoS článku

000550818600001

EID výsledku v databázi Scopus

2-s2.0-85088384561