Variational principles, Lie point symmetries, and similarity solutions of the vector Maxwell equations in nonlinear optics

DOI10.1016/j.physd.2003.10.014zbMath1076.78011OpenAlexW2166017072WikidataQ61637300 ScholiaQ61637300MaRDI QIDQ1888023

Mads Peter Sørensen, Aramis R. Zakharian, Jerome V. Moloney, Moysey Brio, Garry M. Webb

Publication date: 22 November 2004

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physd.2003.10.014

zbMATH Keywords

nonlinear opticstraveling wavessimilarity solutionsvector Maxwell equations

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) Variational principles in infinite-dimensional spaces (58E30) NLS equations (nonlinear Schrödinger equations) (35Q55) Lasers, masers, optical bistability, nonlinear optics (78A60) Geometric theory, characteristics, transformations in context of PDEs (35A30) Foundations in optics and electromagnetic theory (78A02)

Uses Software

• dverk

Cites Work

• An operator approach to Poisson brackets
• Comparisons between Maxwell's equations and an extended nonlinear Schrödinger equation
• Comparison between staggered and unstaggered finite-difference time-domain grids for few-cycle temporal optical soliton propagation
• Solitary waves, steepening and initial collapse in the Maxwell-Lorentz system
• Hamiltonian description of the ideal fluid
• Prolongation structures of nonlinear evolution equations
• A simple model of the integrable Hamiltonian equation
• Geometric Approach to Invariance Groups and Solution of Partial Differential Systems
• Symmetries and differential equations
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