Explicit Peakon solutions to a family of wave-breaking equations

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Explicit Peakon solutions to a family of wave-breaking equations

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Explicit Peakon solutions to a family of wave-breaking equations

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2019

Kód důvěrnosti údajů

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

Název periodika

Journal of Applied Analysis and Computation

ISSN

2156-907X

e-ISSN

—

Svazek periodika

9

Číslo periodika v rámci svazku

5

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

12

Strana od-do

1987-1998

Kód UT WoS článku

000489228300022

EID výsledku v databázi Scopus

2-s2.0-85073516432