Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some mathematical problems in a neoclassical theory of electric charges   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.

12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci