Nondissipative and Dissipative Discontinuity Structures in Solutions to Equations of Micropolar Magnetoelastic Medium

Numerical solutions to magnetoelasticity equations are considered. A numerical scheme based on central differences for spatial derivatives and the fourth-order Runge–Kutta method for time derivatives is used. The initial data is a smoothed step (Riemann problem). The boundaries of existence of discontinuity structures of various types are determined. A method for calculating a structure with emission and an internal weak discontinuity is developed. It is found that in the most general form the formulation of the Riemann problem assumes the presence of oscillatory states, and the corresponding calculations are made.