Nonlinear surface waves on a tangential discontinuity in magnetohydrodynamics

We derive an asymptotic equation that describes the propagation of weakly nonlinear surface waves on a tangential discontinuity in incompressible magnetohydrodynamics. The equation is similar to, but simpler than, previously derived asymptotic equations for weakly nonlinear Rayleigh waves in elasticity. The most interesting feature of the surface waves is that their nonlinear self-interaction is nonlocal.