Periodic solutions and homoclinic solutions for a Swift-Hohenberg equation with dispersion

DOI10.3934/dcdss.2016068zbMath1355.34067OpenAlexW2557231385MaRDI QIDQ728074

Shengfu Deng

Publication date: 22 December 2016

Published in: Discrete and Continuous Dynamical Systems. Series S (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcdss.2016068

zbMATH Keywords

periodic solutionhomoclinic solutionzero-Hopf bifurcationSwift-Hohenberg

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Bifurcation theory for ordinary differential equations (34C23) Bifurcations in context of PDEs (35B32) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Traveling wave solutions (35C07) Higher-order parabolic systems (35K41)

Related Items

Existence of generalized homoclinic solutions for a modified Swift-Hohenberg equation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Generalized homoclinic solutions for the Swift-Hohenberg equation
• Exact solutions of the Swift-Hohenberg equation with dispersion
• Homoclinic solutions for Swift-Hohenberg and suspension bridge type equations
• On the existence of quasipattern solutions of the Swift-Hohenberg equation
• Instability and stability of rolls in the Swift-Hohenberg equation
• Pattern selection of solutions of the Swift--Hohenberg equation
• Interfaces between rolls in the Swift-Hohenberg equation
• Existence of quasipattern solutions of the Swift-Hohenberg equation
• Predicting the bifurcation structure of localized snaking patterns
• The Swift-Hohenberg equation with a nonlocal nonlinearity
• Spots in the Swift--Hohenberg Equation
• Multi-hump solutions with small oscillations at infinity for stationary Swift–Hohenberg equation
• Splitting of separatrices for the Hamiltonian-Hopf bifurcation with the Swift–Hohenberg equation as an example
• Snakes, Ladders, and Isolas of Localized Patterns
• To Snake or Not to Snake in the Planar Swift–Hohenberg Equation
• Rigorous Numerics for Global Dynamics: A Study of the Swift--Hohenberg Equation
• Non-reversible perturbations of homoclinic snaking scenarios
• Fast and stable contour integration for high order divided differences via elliptic functions
• A New Resonance Mechanism in the Swift--Hohenberg Equation with Time-Periodic Forcing
• Some Canonical Bifurcations in the Swift–Hohenberg Equation
• Global branches of multi-bump periodic solutions of the Swift-Hohenberg equation