Asymptotic Dynamics of Locally Oblique Solitary Wave Solutions of the KP Equation

We study asymptotic solutions of the KP equation whose local structure is that of an oblique solitary wave. We derive asymptotic dynamics of the wavefront X = S(Y,T) along which the solitary waves are concentrated. The leading order dynamics of this wavefront is described by a nonlinear hyperbolic equation whose validity breaks down when the nonlinearity induces discontinuities in S_ {Y}. We find a limit in which the dynamics can be continued as a shock, inducing the formation of a wake that trails behind the front. The energy dissipated by the shock is deposited into the wake, preserving the overall energy balance.