Soliton dynamics for the general Degasperis-Procesi equation

2017/12/12 by Georgy Omel'yanov, Omel'yanov, Georgy
Mathematics · #35D30 #35Q53 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35D30 #msc:35Q53

paper · pdf · doi:10.48550/arxiv.1712.04410

13 pages, 3 figures

arxiv created 2017/12/12 · arxiv updated 2017/12/13

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.

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