Spherical nonlinear pulses for the solutions of nonlinear wave equations II, nonlinear caustic*

This article discusses spherical pulse like solutions of the system of semilinear wave equations with the pulses focusing at a point and emerging outgoing in three space variables. In small initial data case, it shows that the nonlinearities have a strong effect at the focal point. Scattering operator is introduced to describe the caustic crossing. With the aid of the L∞ norms, it analyzes the relative errors in approximate solutions.