Diffractive short pulse asymptotics for nonlinear wave equations

We present an algorithm for constructing approximate solutions to nonlinear wave propagation problems in which diffractive effects and nonlinear effec ts come into play on the same time scale. The approximate solutions describ e the propagation of short pulses. In a separate paper the equations used t o construct the approximate solutions are derived using the method of multi ple scales and the approximate solutions are proved accurate in the short w avelength limit. We present numerical studies which even in the linear case indicate significant qualitative differences between these approximations and those derived using the slowly varying envelope ansatz. (C) 2000 publis hed by Elsevier Science B.V. All rights reserved.