Analytic solitary waves of nonintegrable equations

DOI10.1016/S0167-2789(03)00069-1zbMath1098.74615arXivnlin/0302051MaRDI QIDQ1811833

Robert Conte, Micheline Musette

Publication date: 17 June 2003

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

Full work available at URL: https://arxiv.org/abs/nlin/0302051

zbMATH Keywords

ellipticitycubic complex one-dimensional Ginzburg-Landau equationfirst order autonomous ordinary differential equation

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Solitary waves in solid mechanics (74J35)

Related Items (21)

Classifying algebraic invariants and algebraically invariant solutions ⋮ Exact Meromorphic Stationary Solutions of the Real Cubic Swift-Hohenberg Equation ⋮ Meromorphic traveling wave solutions of the complex cubic-quintic Ginzburg-Landau equation ⋮ Detection and construction of an elliptic solution of the complex cubic-quintic Ginzburg-Landau equation ⋮ Meromorphic solutions of autonomous ordinary differential equations without the finiteness property ⋮ Characterizations of all real solutions for the KdV equation and \(W_{\mathbb{R}}\) ⋮ ANALYTIC PATTERNS FOR CHAOTIC EQUATIONS ⋮ From Laurent series to exact meromorphic solutions: The Kawahara equation ⋮ All meromorphic traveling waves of cubic and quintic complex Ginzburg-Landau equations ⋮ Front propagation into unstable states ⋮ Construction of exact partial solutions of nonintegrable systems by means of formal Laurent and Puiseux series ⋮ Elliptic traveling waves of the Olver equation ⋮ Simplest equation method to look for exact solutions of nonlinear differential equations ⋮ Elliptic solutions in the Hénon-Heiles model ⋮ Elliptic General Analytic Solutions ⋮ Solution of paraxial wave equation for inhomogeneous media in linear and quadratic approximation ⋮ On integrability of nonautonomous nonlinear Schrödinger equations ⋮ Meromorphic solutions of a third order nonlinear differential equation ⋮ Proof of the absence of elliptic solutions of the cubic complex Ginzburg-Landau equation ⋮ Non-existence of elliptic travelling wave solutions of the complex Ginzburg--Landau equation ⋮ Construction of Special Solutions for Nonintegrable Systems

Uses Software

• algcurves

Cites Work

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• Sources, sinks and wavenumber selection in coupled CGL equations and experimental implications for counter-propagating wave systems
• The Painlevé property for partial differential equations
• Nonlinear Schrödinger equation including growth and damping
• Painleve analysis and Backlund transformation in the Kuramoto-Sivashinsky equation
• The two-singular-manifold method: I. Modified Korteweg-de Vries and sine-Gordon equations
• Analytic expressions of hydrothermal waves

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