Painlevé analysis of the damped, driven nonlinear Schrödinger equation

DOI10.1017/S0308210500026718zbMath0681.35077MaRDI QIDQ4730192

Peter A. Clarkson

Publication date: 1988

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

zbMATH Keywords

nonlinear Schrödinger equationPainlevé analysiscompletely integrable

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Partial differential equations of mathematical physics and other areas of application (35Q99) Geometric theory, characteristics, transformations in context of PDEs (35A30)

Related Items (18)

On the Integrability of the Poisson Driven Stochastic Nonlinear Schrödinger Equations ⋮ Some exact solutions of the variable coefficient Schrödinger equation ⋮ Integrability and soliton solutions for an \(N\)-coupled nonlinear Schrödinger system in optical fibers ⋮ Looking at a nonlinear inhomogeneous optical fiber through the generalized higher-order variable-coefficient Hirota equation ⋮ The direct symmetry method and its application in variable coefficients Schrödinger equation ⋮ Integrable aspects and applications of a generalized inhomogeneous \(N\)-coupled nonlinear Schrödinger system in plasmas and optical fibers via symbolic computation ⋮ INTEGRABLE ASPECTS AND SOLITON-LIKE SOLUTIONS OF AN INHOMOGENEOUS COUPLED HIROTA–MAXWELL–BLOCH SYSTEM IN OPTICAL FIBERS WITH SYMBOLIC COMPUTATION ⋮ Smoothing properties for systems of nonlinear Schrödinger equations ⋮ Singularity structure analysis of inhomogeneous Hirota and higher order nonlinear Schrödinger equations ⋮ Nonintegrable reductions of the self-dual Yang–Mills equations in a metric of plane wave type ⋮ A modified WTC algorithm for the Painlevé test of nonlinear variable-coefficient PDEs ⋮ Integrable NLS equation with time-dependent nonlinear coefficient and self-similar attractive BEC ⋮ Darboux covariant soliton equations of inhomogeneous type ⋮ Integrable heterogeneous nonlinear Schrödinger equations with dielectric loss: Lie–Bäcklund symmetries ⋮ Solution of paraxial wave equation for inhomogeneous media in linear and quadratic approximation ⋮ On integrability of nonautonomous nonlinear Schrödinger equations ⋮ Integrability aspects of NLS-MB system with variable dispersion and nonlinear effects ⋮ Considerations on conserved quantities and boundary conditions of the \(2 + 1\)-dimensional nonlinear Schrödinger equation

Cites Work

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• The Painlevé property for partial differential equations
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• A connection between nonlinear evolution equations and ordinary differential equations of P-type. I
• Perturbations of Solitons and Solitary Waves
• The inverse scattering transform: Semi-infinite interval
• Nonlinear tunnelling
• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
• Two-dimensional self-modulation of lower hybrid waves in inhomogeneous plasmas
• Soliton Evolution in the Presence of Perturbation

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