5 papers
On dispersive estimates for one-dimensional Klein-Gordon equations
Elena Kopylova
We improve previous results on dispersive decay for 1D Klein- Gordon equation. We develop a novel approach, which allows us to establish the decay in more strong norms and weaken t…
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…
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 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…
On stability of solitons for 3D Maxwell-Lorentz equations with spinning particle
Alexander Komech, Elena Kopylova
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 cons…