Reflection of conormal pulse solutions to large variable-coefficient semilinear hyperbolic systems

We provide a rigorous justication of nonlinear geometric optics expansions for reflecting pulses in space dimensions n > 1. The pulses arise as solutions to variable coefficient semilinear first-order hyperbolic systems. The justification applies to N x N systems with N interacting pulses which depend on phases that may be nonlinear. The coherence assumption made in a number of earlier works is dropped. We consider problems in which incoming pulses are generated from pulse boundary data as well as problems in which a single outgoing pulse reflects off a possibly curved boundary to produce a number of incoming pulses. Although we focus here on boundary problems, it is clear that similar results hold by similar methods for the Cauchy problem for N x N systems in free space. (c) 2024 Elsevier Inc. All rights reserved.