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

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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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.

Information

Published: October, 2004
First available in Project Euclid: 27 October 2004

zbMATH: 1094.35081
MathSciNet: MR2124490

Subjects:
Primary: 35B25 , 35B33 , 35B40 , 35C20 , 35L05 , 35L60 , 35L70 , 35Q60 , 78A45

Keywords: Caustic , focusing , geometric optics , high frequency asymptotics , nonlinear scattering , short pulses

Rights: Copyright © 2004 Departamento de Matemáticas, Universidad Autónoma de Madrid

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