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

@inproceedings{Carles2004FocusingOS,
  title={Focusing of spherical nonlinear pulses in \$\{\mathbb R\}^\{1+3\}\$, II. Nonlinear caustic},
  author={R{\'e}mi Carles and Jeffrey Rauch},
  year={2004}
}
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. 

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