Propagation of a wave beam in a moving medium with a thermal nonlinearity

An analysis is made of the problem of propagation of a wave beam in a moving (circulating) medium under thermal self-interaction conditions. An analytic method is developed for solving the wave equation in the case of a one-dimensional collimated beam. This method is based on reduction of a nonlinear parabolic equation to a nonlinear integrodifferential equation of the Schrödinger type. Analytic solutions are obtained for the wave equation in the case of one-dimensional focusing of the beam and also for the same beam scanning a medium at a constant low velocity. The conditions for guided (self-channeled) propagation of a one-dimensional beam are considered for a model continuous-flow homogeneous medium under thermal self-interaction conditions.