ABSTRACT
Evolution of magnetoacoustic (MA) waves in the heat-releasing plasma is analyzed. Due to the temperature and density dependence of the heating and cooling processes, the dispersion properties of MA waves in the considered medium is rather specific. The dispersion of phase velocity can be either positive or negative, and waves can be further damped or amplified. The amplification of MA waves takes place in the case of isentropic instability. In order to analyze waves in such a medium, we use an approach based on an analogy between nonequilibrium relaxing gas and heat-releasing plasma. The uncompensated isentropic instability restricts the applicability of linear equations describing evolution of magnetoacoustic waves. It appears that for a stabilization of the isentropic instability to be reached, the inclusion of quadratic nonlinear terms is sufficient. In the current research, we derive the nonlinear magnetoacoustic equation (NMAE), which can describe evolution of fast and slow MA waves. The obtained nonlinear equation is different from the known analogues used for the analysis of waves in the considered type of medium, which are modifications of Korteweg-de Vries or Burgers equations. In contrast to the known analogues, it is obtained without the restrictions on wave spectrum and takes into account the main features of nonadiabatic processes that affect the formation of stationary wave structures. We describe analytical solutions of this equation in the form of shock waves including the self-sustained (autowave) pulse and investigate the dependence of these waves on the direction and magnitude of the external magnetic field. The evolutionary stability of the obtained structures is confirmed with the help of numerical solutions of the NMAE. The applicability of NMAE and the correctness of its solutions have been confirmed by the numerical solution of the initial system of magnetohydrodinamic equations. It is shown that the self-sustained (autowave) pulses, which may be realized only in the case of isentropic instability, completely recover their shape after the collision.
