Long-range interaction of four-vector field solitons of Minkowski space

The interaction of solitons of a system of nonlinear equations at distances greatly exceeding their characteristic dimensions is studied by perturbation methods. The slow modulation of soliton parameters under the influence of a small perturbing field of distant solitons is considered. It is shown that the equation of the soliton trajectory in the first and second orders of the method has the form of the classical equation of motion of a particle in electromagnetic and gravitational (in the sense of the bimetrie theory) fields.