On orbital stability of solitons for 2D Maxwell-Lorentz equations

TL;DR

This paper proves the orbital stability of soliton solutions in the 2D Maxwell-Lorentz system with an extended charged particle, using Hamiltonian reduction and a lower bound argument.

Contribution

It introduces a novel stability proof for solitons in the 2D Maxwell-Lorentz equations by employing Hamiltonian reduction and canonical transformations.

Findings

Solitons are orbitally stable under the 2D Maxwell-Lorentz system.

The stability proof relies on a lower bound for the Hamiltonian.

Solitons correspond to uniform motion and rotation of the charged particle.

Abstract

We prove the orbital stability of soliton solutions for 2D Maxwell--Lorentz system with extended charged particle. The solitons corresponds to the uniform motion and rotation of the particle. We reduce the corresponding Hamilton system by the canonical transformation via transition to a comoving frame. The solitons are the critical points of the reduced Hamiltonian. The key point of the proof is a lower bound for the Hamiltonian.