The solution of wave equations for the movind elementary charge with non trivial boundary conditions and the radiation arising in this case is considered. The solution is based on the wave approach gives the adequate description of the phenomenon of transformation of an electromagnetic field of the moving charge at crossing the interface between media with different dielectric properties - solution for the transition radiation. Given solution included the transition radiation near to a trajectory of movement, that essentially develops the theory of transition radiation and opens opportunities of research of more thin effects.
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