Simulation of Domain Walls: Simple Waves in the Magnetodynamics Equation

A partial differential equation modeling the motion of a domain wall taking into account external magnetic fields and damping is considered. In the case of constant coefficients, this equation has a set of trivial solutions—equilibria. Solutions in the form of simple (traveling) waves that correspond to a dynamic transition from one equilibrium to another are studied. Possible types of waves that are stable in linear approximation are listed. A method for calculating the velocity of such waves is given.