In 1920 Schrodinger inspired by ideas of de Broglie on the material wave introduced his wave mechanics in which a particle is modeled by a wave packet. As it was pointed out by M. Born the interpretation of a particle by a wave packet has problems: the wave packets must in course of time become dissipated, and on the other hand the description of the interaction of two electrons as a collision of two wave packets in ordinary three-dimensional space lands us in grave difficulties. To address those problems 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 a spatially localized solitary wave which is an exact solution to the Euler-Lagrange equations which are reduced to a certain nonlinear Schrodinger equation. We show that the wave-corpuscle remains spatially localized when it is free or even when it accelerates in a homogeneous electric field. Two or more interacting charges are well defined even when they collide. (joint work with A. Babin)