Non-interlacing peakon solutions of the Geng-Xue equation

TL;DR

This paper derives explicit formulas for non-interlacing peakon solutions of the Geng-Xue equation, a two-component generalization of a nonlinear wave equation, and analyzes their long-term behavior.

Contribution

It introduces a method to generate arbitrary peakon configurations by transforming interlacing solutions, expanding the understanding of solution structures for the Geng-Xue equation.

Findings

Explicit formulas for non-interlacing peakon solutions

Ability to configure peakons in arbitrary arrangements

Analysis of large-time asymptotic behavior

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.