Propagating fronts and the center manifold theorem

DOI10.1007/BF02100026zbMath0790.34045OpenAlexW2027451299MaRDI QIDQ1174225

Jean-Pierre Eckmann, C. Eugene Wayne

Publication date: 25 June 1992

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

Full work available at URL: https://doi.org/10.1007/bf02100026

zbMATH Keywords

center manifold theoremstationary solutionsSwift-Hohenberg equationamplitude equationpropagating front solutionsfront solutionslowest order approximationtwo-dimensional system of ordinary differential equations

Mathematics Subject Classification ID

Periodic solutions to PDEs (35B10) Wave equation (35L05) Invariant manifolds for ordinary differential equations (34C45)

Related Items

Dynamics and invariant manifolds for a nonlocal stochastic Swift-Hohenberg equation, Modulating traveling fronts in a dispersive Swift-Hohenberg equation coupled to an additional conservation law, Dynamical behaviors of stochastic local Swift-Hohenberg equation on unbounded domain, Modulating traveling fronts for the Swift-Hohenberg equation in the case of an additional conservation law, Growing patterns, Front selection in reaction-diffusion systems via diffusive normal forms, Invariant manifolds for the thin film equation, Time dependent center manifold in PDEs, Existence and approximation of manifolds for the Swift-Hohenberg equation with a parameter, Existence and homogenisation of travelling waves bifurcating from resonances of reaction-diffusion equations in periodic media, Asymptotic dynamical difference between the nonlocal and local Swift–Hohenberg models, Center manifolds without a phase space, Nonlinear Stability of Bifurcating Front Solutions for the Taylor-Couette Problem, Nonlinear Stability of Bifurcating Front Solutions for the Taylor-Couette Problem, Modulated traveling fronts for a nonlocal Fisher-KPP equation: a dynamical systems approach, Approximation of random invariant manifolds for a stochastic Swift-Hohenberg equation, A smooth center manifold theorem which applies to some ill-posed partial differential equations with unbounded nonlinearities, Fronts, domain walls and pulses in a generalized Ginzburg-Landau equation, Invasion Fronts Outside the Homoclinic Snaking Region in the Planar Swift--Hohenberg Equation, Front solutions for the Ginzburg-Landau equation, A center-stable manifold theorem for differential equations in Banach spaces, The time dependent amplitude equation for the Swift-Hohenberg problem, Representation of manifolds for the stochastic Swift-Hohenberg equation with multiplicative noise, On radial solutions of the Swift-Hohenberg equation, Existence and stability of modulating pulse-solutions in a phenomenological model of nonlinear optics, Existence and regularity of invariant graphs for cocycles in bundles: partial hyperbolicity case, The Validity of Generalized Ginzburg-Landau Equations

Cites Work

• The application of centre manifolds to amplitude expansions. I. Ordinary differential equations
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• Multidimensional nonlinear diffusion arising in population genetics
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• Nonlinearly Resonant Surface Waves and Homoclinic Bifurcation
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