Notes on homoclinic solutions of the steady Swift-Hohenberg equation

DOI10.1007/s11401-013-0801-0zbMath1291.34078OpenAlexW1964355530MaRDI QIDQ2448451

Shengfu Deng, Xiaopei Li, Bo-ling Guo

Publication date: 30 April 2014

Published in: Chinese Annals of Mathematics. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11401-013-0801-0

zbMATH Keywords

normal formhomoclinic solutionsreversibility

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Symmetries, invariants of ordinary differential equations (34C14) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Boundary value problems on infinite intervals for ordinary differential equations (34B40)

Related Items (2)

Multi-hump solutions with small oscillations at infinity for stationary Swift–Hohenberg equation ⋮ Existence of generalized homoclinic solutions for a modified Swift-Hohenberg equation

Cites Work

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• Perturbed homoclinic solutions in reversible 1:1 resonance vector fields
• Homoclinic solutions for Swift-Hohenberg and suspension bridge type equations
• Pattern selection of solutions of the Swift--Hohenberg equation
• Multitransition kinks and pulses for fourth order equations with a bistable nonlinearity
• Attractor bifurcation and final patterns of the \(N\)-dimensional and generalized Swift-Hohenberg equations
• Elemental mechanisms of hydrodynamic instabilities
• Attractors for modulation equations on unbounded domains-existence and comparison
• On hydrodynamic instabilities, chaos and phase transition
• Homoclinic Solutions for Fourth Order Traveling Wave Equations
• Pattern formation outside of equilibrium
• Global branches of multi-bump periodic solutions of the Swift-Hohenberg equation

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