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Explicit Peakon solutions to a family of wave-breaking equations
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SYSNO ASEP 0509963 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Explicit 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, ORCIDSource Title Journal of Applied Analysis and Computation - ISSN 2156-907X
Roč. 9, č. 5 (2019), s. 1987-1998Number of pages 12 s. Language eng - English Country US - United States Keywords wave-breaking equations ; singular wave solutions ; peakon solutions ; singular line Subject RIV BA - General Mathematics OECD category Applied mathematics Method of publishing Limited access Institutional support MU-W - RVO:67985840 UT WOS 000489228300022 EID SCOPUS 85073516432 DOI 10.11948/20190061 Annotation The 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. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2020 Electronic address http://dx.doi.org/10.11948/20190061
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