Soliton Dynamics for the General Degasperis–Procesi Equation

Georgy Omel’yanov

doi:10.1007/978-3-030-04459-6_43

Soliton Dynamics for the General Degasperis–Procesi Equation

Georgy Omel’yanov^*

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

We consider the general Degasperis–Procesi model of shallow water out-flows. This fife parametric family of conservation laws contains, in particular, KdV, Camassa–Holm, and Degasperis–Procesi equations. The main result consists of a criterion which guarantees the existence of a smooth soliton-type solution. We discuss also the scenario of soliton interaction for this model in the nonintegrable case.

Original language	English
Title of host publication	Trends in Mathematics
Publisher	Springer International Publishing
Pages	445-454
Number of pages	10
DOIs	https://doi.org/10.1007/978-3-030-04459-6_43
State	Published - 2019

Publication series

Name	Trends in Mathematics
ISSN (Print)	2297-0215
ISSN (Electronic)	2297-024X

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© Springer Nature Switzerland AG 2019.

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10.1007/978-3-030-04459-6_43

Cite this

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AB - We consider the general Degasperis–Procesi model of shallow water out-flows. This fife parametric family of conservation laws contains, in particular, KdV, Camassa–Holm, and Degasperis–Procesi equations. The main result consists of a criterion which guarantees the existence of a smooth soliton-type solution. We discuss also the scenario of soliton interaction for this model in the nonintegrable case.

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Soliton Dynamics for the General Degasperis–Procesi Equation

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