Focusing of spherical nonlinear pulses in ${\mathbb R}^{1+3}$, II. Nonlinear caustic
Rémi Carles and Jeffrey Rauch
Source: Rev. Mat. Iberoamericana Volume 20, Number 3
(2004), 815-864.
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.
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Keywords: Geometric optics; short pulses; focusing; caustic; nonlinear scattering; high frequency asymptotics
Full-text: Open access
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Permanent link to this document: http://projecteuclid.org/euclid.rmi/1098885436
Mathematical Reviews number (MathSciNet): MR2124490
Zentralblatt MATH identifier: 02156859
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