Point charge in the Born-Infeld electrodynamics

We show that the nonlinear Born-Infeld field equations supplemented by the "dynamical condition" (a certain boundary condition for the field along the particle's trajectory) define a perfectly deterministic theory, i.e. a particle's trajectory is determined without any equations of motion. This is a first step towards constructing the consistent theory of point particles interacting with nonlinear electromagnetism. (C) 1998 Elsevier Science B.V.