Multitransition kinks and pulses for fourth order equations with a bistable nonlinearity

DOI10.1016/j.anihpc.2003.03.001zbMath1073.34044OpenAlexW2145255507MaRDI QIDQ1888402

Denis Bonheure

Publication date: 23 November 2004

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIHPC_2004__21_3_319_0

zbMATH Keywords

Swift-Hohenberg equationMinimizationMultitransition heteroclinics and homoclinicsSaddle-focus equilibrium

Mathematics Subject Classification ID

Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (12)

Generalized homoclinic solutions for the Swift-Hohenberg equation ⋮ Wide oscillation finite time blow up for solutions to nonlinear fourth-order differential equations ⋮ Multi-hump solutions with small oscillations at infinity for stationary Swift–Hohenberg equation ⋮ Qualitative behavior of global solutions to some nonlinear fourth order differential equations ⋮ Blow up oscillating solutions to some nonlinear fourth order differential equations ⋮ Notes on homoclinic solutions of the steady Swift-Hohenberg equation ⋮ On the finite space blow up of the solutions of the Swift-Hohenberg equation ⋮ Existence of travelling wave front solutions of a two-dimensional anisotropic model ⋮ Closed characteristics on singular energy levels of second-order Lagrangian systems ⋮ One-dimensional symmetry and Liouville type results for the fourth order Allen-Cahn equation in \(\mathbb{R}^N\) ⋮ EXISTENCE AND UNIQUENESS OF WEAK AND CLASSICAL SOLUTIONS FOR A FOURTH-ORDER SEMILINEAR BOUNDARY VALUE PROBLEM ⋮ Refined blow-up results for nonlinear fourth order differential equations

Cites Work

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• Homoclinic solutions for Swift-Hohenberg and suspension bridge type equations
• Homotopy classes for stable connections between Hamiltonian saddle-focus equilibria
• Heteroclinic connections between nonconsecutive equilibria of a fourth order differential equation
• Multitransition homoclinic and heteroclinic solutions of the extended Fisher-Kolmogorov equation
• Spatial patterns described by the extended Fisher-Kolmogorov (EFK) equation: Kinks
• A topological shooting method and the existence of kinks of the extended Fisher-Kolmogorov equation
• The phase-plane picture for a class of fourth-order conservative differential equations
• Equivalent Norms for Sobolev Spaces
• Global branches of multi-bump periodic solutions of the Swift-Hohenberg equation

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