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

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.