arXiv subjects
Publications and source records attributed to Valeriy Imaykin.
We study the question of global attraction, in the energy norm, for finite energy solutions to classical particle coupled to a scalar wave field. The attraction could take place to either the set of the stationary solutions in the case of a confining potential or to the soliton manifold in the case of zero potential. By energy conservation argument we establish that in both cases there is no global attraction.
We consider the system of Maxwell equations and Lorentz torque equation which describes a motion of charge in electromagnetic field. Under certain symmetry conditions on charge distribution and on initial fields the mass center of the charge remains fixed and the charge rotates around it. The system admits stationary soliton-type solutions. We study the Lyapunov and the orbital stability of the solitons exploiting the energy conservation law. We also show, by the angular momentum argument, that there is no attraction to a soliton of finite angular momentum on the surface of states of the same angular momentum. The bibliography: 23 refs.
We extend the Noether theory of invariants to the Poincare equations. We apply this extension to the Maxwell-Lorentz equations coupled to the Abraham rotating extended electron with the configuration space SO(3).
We justify the Hamilton least action principle for the Maxwell-Lorentz equations with Abraham's rotating extended electron. The main novelty in the proof is application of the variational Poincare equations on the Lie group SO(3). The variational equations allow to derive the corresponding conservation laws from general Noether theory of invariants.