An explicit description of the global attractor of the damped and driven sine-Gordon equation

DOI10.1007/BF02101747zbMath0805.35122WikidataQ62570080 ScholiaQ62570080MaRDI QIDQ1328227

Rainer Grauer, Björn Birnir

Publication date: 1 February 1995

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

zbMATH Keywords

bifurcationshyperbolic structuredecomposition of finite-dimensional attractors

Mathematics Subject Classification ID

Attractors and repellers of smooth dynamical systems and their topological structure (37C70) NLS equations (nonlinear Schrödinger equations) (35Q55)

Related Items (11)

Forward controllability of a random attractor for the non-autonomous stochastic sine-Gordon equation on an unbounded domain ⋮ Positive doubly periodic solutions of telegraph equations with delays ⋮ Maximum principles and the method of upper and lower solutions for time-periodic problems of the telegraph equations ⋮ Positive doubly periodic solutions of nonlinear telegraph equations. ⋮ Derivation of the viscous Moore-Greitzer equation for aeroengine flow ⋮ A duality theorem for periodic solutions of a class of second order evolution equations ⋮ The basic attractor and the remainder of homo- and heteroclinic orbits ⋮ Autoresonance in a model of a terahertz wave generator ⋮ Prevalence ⋮ A maximum principle for periodic solutions of the telegraph equation ⋮ Gevrey regularity for the attractor of a partially dissipative model of Bénard convection in a porous medium

Cites Work

• Breather dynamics in the nonlinear Schrödinger regime of perturbed sine-Gordon systems
• Attractors for damped nonlinear hyperbolic equations
• On the concept of attractor
• Applications of centre manifold theory
• The center manifold and bifurcations of damped and driven sine-Gordon breathers
• Embedology
• A quasi-periodic route to chaos in a near-integrable PDE
• Multi-soliton solutions and quasi-periodic solutions of nonlinear equations of sine-Gordon type
• Existence theory and invariant manifolds of bubble clouds
• Complex hill's equation and the complex periodic korteweg-de vries equations
• Singularities of the complex korteweg-de vries flows
• An Example of Blow-Up, for the Complex K<scp>d</scp>V Equation and Existence Beyond the Blow-Up
• The sine-gordon and sinh-gordon equations on the circle
• Correlations between Chaos in a Perturbed Sine-Gordon Equation and a Truncated Model System
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