48 citations · 245 across the 41 of their papers we have counts for
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On soliton asymptotics for Maxwell--Lorentz equations with rotating particle
Elena Kopylova
We consider the 2D Maxwell--Lorentz equations with an extended charged rotating particle. The system admits soliton solutions corresponding to a particle moving with a constant vel…
On orbital stability of solitons for 2D Maxwell-Lorentz equations
Alexander Komech, Elena Kopylova
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 th…
Global attraction to solitons for 2D Maxwell--Lorentz equations with spinning particle
Elena Kopylova, Alexander Komech
We consider the 2D Maxwell--Lorentz system which describes a rotating particle coupled to the Maxwell field. The system admits stationary soliton-type solutions. We prove the attra…
On global attraction to solitons for 3D Maxwell-Lorentz equations
E. A. Kopylova, A. I. Komech
We consider the Maxwell field coupled to a single rotating charge. This Hamiltonian system admits soliton-type solutions, where the field is static, while the charge rotates with c…
Momentum map for the Maxwell-Lorentz equations with spinning particle
Alexander Komech, Elena Kopylova
We develop the theory of momentum map for the Maxwell-Lorentz equations with spinning extended charged particle. This theory is indispensable for the study of long-time behaviour a…
On stability of solid state in the Schrödinger-Poisson-Newton model
Alexander Komech, Elena Kopylova
We survey our recent results on stability of 3D crystals in the Schrödinger-Poisson-Newton model. We establish orbital stability for the ground state in the case of finite crystal…