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

Alexander Komech; Elena Kopylova

doi:10.3934/cpaa.2024012

Article Contents

2024, Volume 23, Issue 3: 325-338. Doi: 10.3934/cpaa.2024012

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

Alexander Komech^1, and
Elena Kopylova^1, ,

1.
Faculty of Mathematics of Vienna University, Vienna, Austria

^*Corresponding author: Elena Kopylova
^*Corresponding author: Elena Kopylova

Received: July 2023

Revised: January 2024

Early access: February 28, 2024

Published online: February 28, 2024

The second author is supported by the Austrian Science Fund (FWF) P34177.

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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.

Keywords:

Mathematics Subject Classification: Primary: 35L70, 35Q61, 37K40; Secondary: 37K06, 47F05, 70S05, 70G65.

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