Interactions of solitary waves in the Adlam-Allen model

TL;DR

This paper investigates the interaction dynamics of solitary waves in the Adlam-Allen plasma model, revealing their exponential repulsion through energetic and Hamiltonian analyses, validated by simulations and connected to KdV solitons.

Contribution

It introduces two analytical approaches to characterize solitary wave interactions in the Adlam-Allen model and compares them with numerical simulations for validation.

Findings

Solitary wave interactions are exponentially repulsive.

Analytical methods match simulation results after adjustments.

Connections to Korteweg--de Vries solitons are established.

Abstract

We study the interactions of two or more solitary waves in the Adlam-Allen model describing the evolution of a (cold) plasma of positive and negative charges, in the presence of electric and transverse magnetic fields. In order to show that the interactions feature an exponentially repulsive nature, we elaborate two distinct approaches: (a) using energetic considerations and the Hamiltonian structure of the model; (b) using the so-called Manton's method. We compare these findings with results of direct simulations, and identify adjustments necessary to achieve a quantitative match between them. Additional connections are made, such as with solitons of the Korteweg--de Vries equation. New challenges are identified in connection to this model and its solitary waves.