Focusing of spherical nonlinear pulses in , II. Nonlinear caustic

  • Rémi Carles

    Université Montpellier 2, France
  • Jeffrey Rauch

    University of Michigan, Ann Arbor, USA

Abstract

We study spherical pulse like families of solutions to semilinear wave equations 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 norm.

Cite this article

Rémi Carles, Jeffrey Rauch, Focusing of spherical nonlinear pulses in , II. Nonlinear caustic. Rev. Mat. Iberoam. 20 (2004), no. 3, pp. 815–864

DOI 10.4171/RMI/408