JournalsrmiVol. 20, No. 3pp. 815–864

Focusing of spherical nonlinear pulses in R1+3{\mathbb R}^{1+3}, II. Nonlinear caustic

  • Rémi Carles

    Université Montpellier 2, France
  • Jeffrey Rauch

    University of Michigan, Ann Arbor, USA
Focusing of spherical nonlinear pulses in ${\mathbb R}^{1+3}$, II. Nonlinear caustic cover
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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 LL^\infty norm.

Cite this article

Rémi Carles, Jeffrey Rauch, Focusing of spherical nonlinear pulses in R1+3{\mathbb R}^{1+3}, II. Nonlinear caustic. Rev. Mat. Iberoam. 20 (2004), no. 3, pp. 815–864

DOI 10.4171/RMI/408