  We study here a number of mathematical problems related to our recently
introduced neoclassical theory for the electromagnetic phenomena in which
charges are represented by complex valued wave functions as in the Schrodinger
wave mechanics. Dynamics of charges in the non-relativistic case is governed by
a system of nonlinear Schrodinger equations coupled with the electromagnetic
fields, and we prove for it that the centers of wave functions converge in
macroscopic regimes to trajectories of points governed by the Newton's
equations with the Lorentz forces provided the wave functions remain localized.
Exact solutions in the form of localized accelerating solitons are found. Our
studies of a class of time multiharmonic solutions of the same field equations
show that they satisfy Planck-Einstein relation and that the energy levels of
the nonlinear eigenvalue problem for the hydrogen atom converge to the
well-known energy levels of the linear Schrodinger operator when the free
charge size is much larger than the Bohr radius.
