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

The result's identifiers

  • Result code in 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>

  • Result on the web

    <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>

Alternative languages

  • Result language

    angličtina

  • Original language name

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

  • Original language description

    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.

  • Czech name

  • Czech description

Classification

  • Type

    J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database

  • CEP classification

  • OECD FORD branch

    10101 - Pure mathematics

Result continuities

  • Project

  • Continuities

    I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Others

  • Publication year

    2020

  • Confidentiality

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

Data specific for result type

  • Name of the periodical

    Studies in Applied Mathematics

  • ISSN

    0022-2526

  • e-ISSN

    1467-9590

  • Volume of the periodical

    145

  • Issue of the periodical within the volume

    3

  • Country of publishing house

    US - UNITED STATES

  • Number of pages

    26

  • Pages from-to

    537-562

  • UT code for WoS article

    000550818600001

  • EID of the result in the Scopus database

    2-s2.0-85088384561