Explicit Peakon solutions to a family of wave-breaking equations

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F19%3A00509963" target="_blank" >RIV/67985840:_____/19:00509963 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.11948/20190061" target="_blank" >http://dx.doi.org/10.11948/20190061</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.11948/20190061" target="_blank" >10.11948/20190061</a>

Result language
angličtina
Original language name
Explicit Peakon solutions to a family of wave-breaking equations
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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