Analytic solitary waves of nonintegrable equations

Abstract

Even if it is nonintegrable, a differential equation may nevertheless admit particular solutions which are globally analytic. On the example of the dynamical system of Kuramoto and Sivashinsky, which is generically chaotic and presents a high physical interest, we review various methods, all based on the structure of singularities, allowing us to characterize the analytic solution which depends on the largest possible number of constants of integration.

LaTex 2e. To appear, Physica D

References in corpus (3)

• The Building Blocks of Spatiotemporal Intermittency
• Sources, sinks and wavenumber selection in coupled CGL equations and experimental implications for counter-propagating wave systems
• Analytic expressions of hydrothermal waves

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• From Laurent Series to Exact Meromorphic Solutions: the Kawahara equation
• Elliptic general analytic solutions
• Meromorphic solutions of a third order nonlinear differential equation
• Solitary waves of nonlinear nonintegrable equations
• On elliptic solutions of the quintic complex one-dimensional Ginzburg-Landau equation
• Exact meromorphic stationary solutions of the real cubic Swift-Hohenberg equation
• On elliptic solutions of the cubic complex one-dimensional Ginzburg-Landau equation
• Meromorphic traveling wave solutions of the complex cubic-quintic Ginzburg-Landau equation
• On two nonintegrable cases of the generalized Henon-Heiles system with an additional nonpolynomial term
• Construction of Special Solutions for Nonintegrable Systems
• Detection and construction of an elliptic solution to the complex cubic-quintic Ginzburg-Landau equation
• New solutions to the complex Ginzburg-Landau equations
• All meromorphic traveling waves of cubic and quintic complex Ginzburg-Landau equations