Focusing of spherical nonlinear pulses in \(\mathbb R^{1+3}\). II: Nonlinear caustic
type: Item
instance of: scholarly article
title: Focusing of spherical nonlinear pulses in \(\mathbb R^{1+3}\). II: Nonlinear caustic
zbMATH Open document ID: 1094.35081
DOI: 10.4171/RMI/408
author: Rémi Carles
author: Jeffrey Rauch
published in: Revista Matemática Iberoamericana
publication date: 2005-04-15T00:00:00Z
full work available at URL: https://eudml.org/doc/39728
review text: Summary: For parts I and III see [Proc. Am. Math. Soc. 130, No. 3, 791--804 (2002; Zbl 0953.35089) and Tôhoku Math. J. (2) 56, No. 3, 393--410 (2004; Zbl 1095.35010)]. 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.
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35B25
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35C20
Mathematics Subject Classification ID: 35Q60
Mathematics Subject Classification ID: 78A45
Mathematics Subject Classification ID: 78A05
Mathematics Subject Classification ID: 35B33
zbMATH DE Number: 2156859
zbMATH Keywords: high frequency asymptotics
zbMATH Keywords: semilinear wave equations
zbMATH Keywords: scattering operator
MaRDI profile type: Publication
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OpenAlex ID: W2006342895
description: scientific article; zbMATH DE number 2156859