Stability of stationary solutions for nonintegrable peakon equations

Hone, Andrew N.W. and Lafortune, Stephane (2014) Stability of stationary solutions for nonintegrable peakon equations. Physica D: Nonlinear Phenomena, 269 . pp. 28-36. ISSN 0167-2789. (doi:https://doi.org/10.1016/j.physd.2013.11.006) (Full text available)

Abstract

The Camassa-Holm equation with linear dispersion was originally derived as an asymptotic equation in shallow water wave theory. Among its many interesting mathematical properties, which include complete integrability, perhaps the most striking is the fact that in the case where linear dispersion is absent it admits weak multi-soliton solutions - "peakons" - with a peaked shape corresponding to a discontinuous first derivative. There is a one-parameter family of generalized Camassa-Holm equations, most of which are not integrable, but which all admit peakon solutions. Numerical studies reported by Holm and Staley indicate changes in the stability of these and other solutions as the parameter varies through the family. In this article, we describe analytical results on one of these bifurcation phenomena, showing that in a suitable parameter range there are stationary solutions - "leftons" - which are orbitally stable.

Item Type: Article
Subjects: Q Science > QA Mathematics (inc Computing science) > QA299 Analysis, Calculus
Q Science > QA Mathematics (inc Computing science) > QA377 Partial differential equations
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science
Depositing User: Andrew N W Hone
Date Deposited: 20 Jun 2014 23:19 UTC
Last Modified: 26 Jun 2017 15:47 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/41484 (The current URI for this page, for reference purposes)
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