Explicit Peakon solutions to a family of wave-breaking equations

0509963 - MÚ 2020 RIV US eng J - Journal Article
Zhang, L. - Zhang, J. - Bai, Y. - Hakl, Robert
Explicit Peakon solutions to a family of wave-breaking equations.
Journal of Applied Analysis and Computation. Roč. 9, č. 5 (2019), s. 1987-1998. ISSN 2156-907X. E-ISSN 2158-5644
Institutional support: RVO:67985840
Keywords : wave-breaking equations * singular wave solutions * peakon solutions * singular line
OECD category: Applied mathematics
Impact factor: 1.573, year: 2019
Method of publishing: Limited access
http://dx.doi.org/10.11948/20190061

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.
Permanent Link: http://hdl.handle.net/11104/0300543