Resumen de Focusing of spherical nonlinear pulses in R 1+3, II. Nonlinear caustic

Jeffrey Rauch, Rémi Carles

• We study spherical pulse like families of solutions to semilinear wave equattions in space time of dimension 1+3 as the pulses focus at a point and emerge outgoing. We emphasize the scales for which the incoming and outgoing waves behave linearly but the nonlinearity has a strong effect at the focus. The focus crossing is described by a scattering operator for the semilinear equation, which broadens the pulses. The relative errors in our approximate solutions are small in the L8 norm.