Discontinuity structures in a micropolar magnetoelastic medium and methods for studying discontinuities in models with dispersion and a finite velocity of the wave propagation

Abstract

We consider solutions of a system of magnetoelasticity equations. As initial data for these solutions, we use data of the smoothed step type (the problem of discontinuity decay). Among these solutions, there are solutions with purely nondissipative structures of the soliton type and structures with the radiated wave and the internal dissipative discontinuities of derivatives. We develop techniques for studying discontinuities in solutions of equations with dispersion and finite of wave propagation velocity. We analyze and justify the existence of such structures by studying equations of traveling waves. We reveal the presence of sequences of weak discontinuities in structures with the radiated wave. We also study a dissipative structure of the shock-wave type. We consider conditions for discontinuities and their evolutionary properties. We establish that when studying the discontinuities in the solutions of dispersion equations, the limiting velocities of short waves play the same role as the characteristic velocities for hyperbolic equations.