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arXiv · 2306.00508

On stability of solitons for 3D Maxwell-Lorentz equations with spinning particle

Alexander Komech·Elena Kopylova
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Abstract

We consider stability of solitons of 3D Maxwell--Lorentz system with extended charged spinning particle.The solitons are solutions which correspond to a particle moving with a constant velocity $v\in\R^3$ with $|v|<1$ and rotating with a constant angular velocity $\omega\in R^3$. Our main results are the orbital stability of moving solitons with $\omega=0$ and a {\it linear} orbital stability of rotating solitons with $v=0$. The Hamilton--Poisson structure of the Maxwell--Lorentz system is degenerate and admits the Casimir invariants. We construct the Lyapunov function as a linear combination of the Hamiltonian with a suitable Casimir invariant. The key point is a lower bound for this function. The proof of the bound in the case $\om\ne 0$ relies on angular momentum conservation and suitable spectral arguments including the Heinz inequality and closed graph theorem.

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Alexander Komech, Elena Kopylova. 2023-06-01. On stability of solitons for 3D Maxwell-Lorentz equations with spinning particle. https://arxiv.org/abs/2306.00508

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