Diiractive Short Pulse Asymptotics for Nonlinear Wave Equations

We present an algorithm for constructing approximate solutions to nonlinear wave propagation problems in which diiractive eeects and nonlinear eeects come into play on the same time scale. The approximate solutions describe the propagation of short pulses. In a separate paper the equations used to construct the approximate solutions are derived using the method of multiple scales and the approximate solutions are proved accurate in the short wavelength limit. We present numerical studies which even in the linear case indicate signiicant qualitative diierences between these approximations and those derived using the slowly varying envelope ansatz.