Modeling and analysis of the large scale magneto hydrodynamics waves

A system of nonlinear partial differential equations is considered that models perturbations in a layer of an ideal electrically conducting rotating fluid bounded by spatially and temporally varying surfaces with allowance for inertial forces and diffusion of magnetic field. The system is reduced to a scalar equation. The solvability of initial boundary value problems arising in the theory of waves in conducting rotating fluids can be established by analyzing this equation.