Wave interactions in magnetohydrodynamics

In this paper, we apply the Majda-Rosales theory of resonantly interacting, weakly nonlinear hyperbolic waves in one space dimension to the equations of magnetohydrodynamics. We write out the general system of resonant interaction equations for magnetohydrodynamics together with normalized triad equations for all possible magnetohydrodynamic triads. We consider both the strictly and the nonstrictly hyperbolic cases and we include both dissipative and dispersive effects. We present some numerical solutions of magnetosonic entropy wave interactions which illustrate the effect of KdV-type dispersion.