Nonlinear effects in the propagation, reflection and refraction of magnetosonic waves

Reflection and refraction of magnetosonic waves in domains of different sound and Alfvén speeds have been often studied by means of the linearized magnetohydrodynamic equations, obtaining a more complex version of Fresnel laws. However, these waves are intrinsically nonlinear and this method does not describe adequately wave interaction. We consider high-frequency waves by means of the geometric optics approximation to follow the waves evolution until the interface is reached, where this procedure fails because the variation of spatial scales is faster than the frequency. It is shown that a connection with a local linear analysis is feasible, thus yielding the full evolution including reflection, transmission and presence of surface waves, as well as the influence of the interface on the time of shock formation.