This article proposes an interpretation of quantum physics based on the theory of solitons. According to this interpretation, an elementary particle (in particular, an electron) is a soliton solution to a system of nonlinear equations, while the linear equations of quantum mechanics for wave functions represent the boundary conditions for the presence of soliton solutions. It is hypothesized that the nonlinear equations for a quantum electron are ordinary Maxwell equations, in which the charge and current densities are expressed through quadratic combinations of electromagnetic field strengths. The complex wave function, which describes the motion of an electron, in this formulation is an ordinary electromagnetic wave, where the real part is the electric field strength, and the imaginary part is the magnetic field strength. Soliton equations, Maxwell's equations and quantum equations are easily written using 3+1 Pauli matrices, which indicates that the 3+1 coordinate system of space and time is a natural implementation of the world of particles - wave solitons. The proposed interpretation allows us to combine both the Copenhagen interpretation and Bohm’s theory of "hidden" variables.