Propagation of electromagnetic waves in a waveguide with nonuniformly moving boundary

The propagation of an elastic wave along the axis of a rectangular waveguide is studied for any type of wave polarization in the case where one of the waveguide walls is moving according to a parabolic law in the direction of the normal to the wall. The propagation of the wave is described by a wave equation with variable coefficients. It is shown that in the waveguide considered, it is not possible to divide the field into TE and TM modes, except for the H-no type wave. An exact solution is obtained to the problem formulated, along with adequate expressions for the electromagnetic field of the wave. The instantaneous frequency and the transverse wave number are related to each other through a simple expression, which is valid for a stationary waveguide.