Solitary Alfv\'en Waves

TL;DR

This paper introduces the solitary Alfvén wave as an exact nonlinear solution of ideal MHD equations and demonstrates its stability through three-dimensional numerical simulations, expanding understanding of nonlinear Alfvénic phenomena.

Contribution

The paper presents the first exact nonlinear solitary Alfvén wave solution and constructs a 3D numerical model called the Alfvénon, confirming its stability under ideal MHD conditions.

Findings

The solitary Alfvén wave is an exact nonlinear solution of ideal MHD.

The Alfvénon model exhibits remarkable stability in simulations.

The wave maintains its structure under ideal MHD evolution.

Abstract

We present the solitary Alfv\'en wave, an exact nonlinear solution of the ideal magnetohydrodynamic (MHD) equations, and construct a three-dimensional numerical model -- an \emph{Alfv\'enon}. The model is characterized by an unperturbed far field, quasi-constant $|\boldsymbol{B}|$, and open field-line topology. Direct MHD simulations of the Alfv\'enon demonstrate remarkable stability, confirming that it behaves as a nonlinear solitary Alfv\'enic solution under ideal MHD evolution.