Non-interlacing peakon solutions of the Geng-Xue equation
Mathematical Physics
2018-12-24 v1 math.MP
Pattern Formation and Solitons
Exactly Solvable and Integrable Systems
Abstract
The aim of the present paper is to derive explicit formulas for arbitrary peakon solutions of the Geng-Xue equation, a two-component generalization of Novikov's cubically nonlinear Camassa-Holm type equation. By performing limiting procedures on the previosly known formulas for so-called interlacing peakon solutions, where the peakons in the two component occur alternatingly, we turn some of the peakons into zero-amplitude "ghostpeakons", in such a way that the remaining ordinary peakons occur in any desired configuration. We also study the large-time asymptotics of these solutions.
Keywords
Cite
@article{arxiv.1812.09173,
title = {Non-interlacing peakon solutions of the Geng-Xue equation},
author = {Budor Shuaib and Hans Lundmark},
journal= {arXiv preprint arXiv:1812.09173},
year = {2018}
}
Comments
133 pages, 25 figures. pdfLaTeX + AMS packages + hyperref + TikZ