Singularly perturbed and nonlocal modulation equations for systems with interacting instability mechanisms

DOI10.1007/BF02678142zbMath0885.58075OpenAlexW2131424747MaRDI QIDQ1368907

Vivi Rottschäfer, Arjen Doelman

Publication date: 26 April 1998

Published in: Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02678142

zbMATH Keywords

singularly perturbed systemslocalized structuresinteracting instability mechanisms

Mathematics Subject Classification ID

Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40)

Related Items (7)

Construction and asymptotic stability of structurally stable internal layer solutions ⋮ Second-order set-valued differential equations with boundary conditions ⋮ Geometric mesh three-point discretization for fourth-order nonlinear singular differential equations in polar system ⋮ Efficient algorithms for fourth and sixth-order two-point non-linear boundary value problems using non-polynomial spline approximations on a geometric mesh ⋮ On the transition from the Ginzburg-Landau equation to the extended Fisher-Kolmogorov equation ⋮ Chaotic traveling wave solutions in coupled Chua's circuits ⋮ Adaptive mesh generation for singularly perturbed fourth-order ordinary differential equations

Cites Work

• Unnamed Item
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• Geometric singular perturbation theory for ordinary differential equations
• Coupled nonlocal complex Ginzburg-Landau equations in gasless combustion
• Global bifurcations and chaos. Analytical methods
• Fronts, pulses, sources and sinks in generalized complex Ginzburg-Landau equations
• The Ginzburg-Landau manifold is an attractor
• Tracking invariant manifolds with differential forms in singularly perturbed systems
• On the validity of the Ginzburg-Landau equation
• Traveling waves in the complex Ginzburg-Landau equation
• The effect of nonlocal interactions on the dynamics of the Ginzburg-Landau equation
• Sustained Resonance for a Nonlinear System with Slowly Varying Coefficients
• Stability of plane wave solutions of complex Ginzburg-Landau equations
• Long-Wave Interactions in Morphological and Convective Instabilities
• On the non-linear mechanics of hydrodynamic stability
• Non-linear Interaction of Morphological and Convective Instabilities During Solidification of a Dilute Binary Alloy
• The interaction of two spatially resonant patterns in thermal convection. Part 1. Exact 1:2 resonance
• A theoretical and experimental study of double-layer convection
• Homoclinic explosions and implosions
• Sand ripples under sea waves Part 3. Brick-pattern ripple formation
• Modulation Equations for Spatially Periodic Systems: Derivation and Solutions
• Existence and stability of singular heteroclinic orbits for the Ginzburg - Landau equation
• Relaxation oscillations including a standard chase on French ducks
• On the validity of mean-field amplitude equations for counterpropagating wavetrains
• Instability of quasiperiodic solutions of the Ginzburg–Landau equation
• Tracking Invariant Manifolds up to Exponentially Small Errors
• Amplitude equations for travelling wave convection

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