Integrable heterogeneous nonlinear Schrödinger equations with dielectric loss: Lie–Bäcklund symmetries

DOI10.1063/1.529099zbMath0734.35132OpenAlexW1993086460MaRDI QIDQ3361310

Philip Broadbridge, S. E. Godfrey

Publication date: 1991

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.529099

zbMATH Keywords

cubic nonlinear Schrödinger equationLie-Bäcklund symmetry

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) NLS equations (nonlinear Schrödinger equations) (35Q55) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Waves and radiation in optics and electromagnetic theory (78A40) Correspondences and other transformation methods (e.g., Lie-Bäcklund) for PDEs on manifolds (58J72)

Related Items (3)

Admissible transformations and normalized classes of nonlinear Schrödinger equations ⋮ All solutions of standard symmetric linear partial differential equations have classical Lie symmetry ⋮ Semiclassical Solutions of the Nonlinear Schrödinger Equation

Cites Work

• Exact solutions of the nonlinear Schrödinger equation in time-dependent parabolic density profiles
• Slowly varying solitary waves. II. Nonlinear Schrödinger equation
• Integrable forms of the one-dimensional flow equation for unsaturated heterogeneous porous media
• On the remarkable nonlinear diffusion equation (∂/∂x)[a (u+b)−2(∂u/∂x)−(∂u/∂t)=0]
• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
• Two-dimensional self-modulation of lower hybrid waves in inhomogeneous plasmas
• Painlevé analysis of the damped, driven nonlinear Schrödinger equation

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