Mathematical Sciences: Shock Waves and Riemann Problem in Magnetohydrodynamics

本文对线性波和非线性波的共振相互作用进行了数值分析研究。当前的目标是借助具有特定对称性的守恒定律的数值、渐近和动力系统，特别是二维和三维磁力线重连的数值模拟，描述模型方程的共振波相互作用及其在激波形成中的作用。

This research is concerned with a numerical and analytical study of resonant interactions of linear and nonlinear waves. The immediate goal is to describe resonant wave interaction for model equations and the role it plays in the formation of shock waves with the help of numerical, asymptotic and dynamical systems of conservation laws with specific symmetries, in particular, to the numerical simulations of magnetic field line reconnection in two and three dimensions.