Variational principles, Lie point symmetries, and similarity solutions of the vector Maxwell equations in nonlinear optics
type: Item
instance of: scholarly article
title: Variational principles, Lie point symmetries, and similarity solutions of the vector Maxwell equations in nonlinear optics
zbMATH Open document ID: 1076.78011
author: Mads Peter Sørensen
author: A. R. Zakharian
author: J. V. Moloney
author: G. M. Webb
author: Moysey Brio
published in: Physica D
publication date: 2004-11-22T00:00:00Z
review text: The authors formulate the vector Maxwell equations coupled to a single Lorentz oscillator with instantaneous Kerr nonlinearity in terms of Lagrangian and Hamiltonian variational principles. Four conservation laws for these equations are obtained. The traveling wave solutions and the kink solutions are investigated. It was obtained that the smooth periodic traveling wave solutions develop very steep electric field gradients as the dimensionless wave velocity tends to 1 from above, and the method of extending them into the slower velocity regime is demonstrated. It was also obtained that the kink and anti-kink solutions exist only for a restricted range of traveling wave velocities. These solutions may be used in switching devices or in optical computing.
Mathematics Subject Classification ID: 78A60
Mathematics Subject Classification ID: 35A30
Mathematics Subject Classification ID: 35Q55
Mathematics Subject Classification ID: 35Q60
Mathematics Subject Classification ID: 58E30
Mathematics Subject Classification ID: 78A02
zbMATH DE Number: 2117600
zbMATH Keywords: nonlinear optics
zbMATH Keywords: vector Maxwell equations
zbMATH Keywords: similarity solutions
zbMATH Keywords: traveling waves
Wikidata QID: Q61637300
describes a project that uses: dverk
MaRDI profile type: Publication
full work available at URL: j.physd.2003.10.014
OpenAlex ID: W2166017072
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DOI: 10.1016/J.PHYSD.2003.10.014
description: scientific article; zbMATH DE number 2117600