  It is well known that a concept of point charge interacting with
electromagnetic (EM) field has a problem. To address that problem we introduce
a concept of wave-corpuscle to describe spinless elementary charges interacting
with the classical EM field. Every charge interacts only with the EM field and
is described by a complex valued wave function over 4-dimensional space time
continuum. A system of many charges interacting with the EM field is defined by
a local, gauge and Lorentz invariant Lagrangian with a key ingredient - a
nonlinear self-interaction term providing for a cohesive force assigned to
every charge. An ideal wave-corpuscle is an exact solution to the
Euler-Lagrange equations describing both free or accelerated motion. It carries
explicitly features of a point charge and the de Broglie wave. A system of well
separated charges moving with nonrelativistic velocities are represented
accurately as wave-corpuscles governed by the Newton motion equations for point
charges interacting with the Lorentz forces. In this regime the nonlinearities
are "stealthy" and don't show explicitly anywhere, but they provide for binding
forces that keep localized every individual charge.
