Numerical interactions between compactons and kovatons of the Rosenau-Pikovsky K(cos) equation

TL;DR

This paper presents a numerical study of the interactions between compactons and kovatons in the Rosenau-Pikovsky K(cos) equation, revealing new phenomena like wave inversion and ripple generation.

Contribution

It introduces a new Padé numerical method to simulate solitary wave interactions and uncovers novel behaviors during wave collisions.

Findings

Observation of wave inversion phenomena.

Detection of ripple generation decomposing into compacton-anticompacton pairs.

Quantitative analysis of self-similar wavepackets.

Abstract

A numerical study of the nonlinear wave solutions of the Rosenau-Pikovsky K(cos) equation is presented. This equation supports at least two kind of solitary waves with compact support: compactons of varying amplitude and speed, both bounded, and kovatons which have the maximum compacton amplitude, but arbitrary width. A new Pad\'e numerical method is used to simulate the propagation and, with small artificial viscosity added, the interaction between these kind of solitary waves. Several numerically induced phenomena that appear while propagating these compact travelling waves are discussed quantitatively, including self-similar forward and backward wavepackets. The collisions of compactons and kovatons show new phenomena such as the inversion of compactons and the generation of pairwise ripples decomposing into small compacton-anticompacton pairs.