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 $L^\infty$ norm.
Citation
Rémi Carles. Jeffrey Rauch. "Focusing of spherical nonlinear pulses in ${\mathbb R}^{1+3}$, II. Nonlinear caustic." Rev. Mat. Iberoamericana 20 (3) 815 - 864, October, 2004.
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