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Explicit Peakon solutions to a family of wave-breaking equations

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    SYSNO ASEP0509963
    Document TypeJ - Journal Article
    R&D Document TypeJournal Article
    Subsidiary JČlánek ve WOS
    TitleExplicit Peakon solutions to a family of wave-breaking equations
    Author(s) Zhang, L. (CN)
    Zhang, J. (CN)
    Bai, Y. (CN)
    Hakl, Robert (MU-W) RID, SAI, ORCID
    Source TitleJournal of Applied Analysis and Computation - ISSN 2156-907X
    Roč. 9, č. 5 (2019), s. 1987-1998
    Number of pages12 s.
    Languageeng - English
    CountryUS - United States
    Keywordswave-breaking equations ; singular wave solutions ; peakon solutions ; singular line
    Subject RIVBA - General Mathematics
    OBOR OECDApplied mathematics
    Způsob publikováníOmezený přístup
    Institutional supportMU-W - RVO:67985840
    UT WOS000489228300022
    EID SCOPUS85073516432
    DOI10.11948/20190061
    AnnotationThe singular traveling wave solutions of a general 4-parameter family equation which unifies the Camass-Holm equation, the Degasperis-Procesi equation and the Novikov equation are investigated in this paper. At first, we obtain the explicit peakon solutions for one of its specific case that a = (p+2)c, b = (p + 1)c and c = 1, which is referred to a generalized Camassa-Holm-Novikov (CHN) equation, by reducing it to a second-order ordinary differential equation (ODE) and solving its associated first-order integrable ODE. By observing the characteristics of peakon solutions to the CHN equation, we construct the peakon solutions for the general 4-parameter breaking wave equation. It reveals that singularities of the peakon solutions come up only when the solutions attain singular points of the equation, which might be a universal principal for all singular traveling wave solutions for wave breaking equations.
    WorkplaceMathematical Institute
    ContactJarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757
    Year of Publishing2020
    Electronic addresshttp://dx.doi.org/10.11948/20190061
Number of the records: 1