Hexagon Invasion Fronts Outside the Homoclinic Snaking Region in the Planar Swift--Hohenberg Equation

DOI10.1137/20M1369622zbMath1470.35051arXiv1911.03983OpenAlexW2969937436MaRDI QIDQ5004087

David J. B. Lloyd

Publication date: 30 July 2021

Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1911.03983

zbMATH Keywords

numerical continuationquadratic-cubic nonlinearityinfinitely many folds

Mathematics Subject Classification ID

Initial-boundary value problems for higher-order parabolic equations (35K35) Bifurcations in context of PDEs (35B32) Homoclinic and heteroclinic orbits for dynamical systems (37C29) Semilinear parabolic equations (35K58) Pattern formations in context of PDEs (35B36)

Uses Software

• Matlab
• wavetrain

Cites Work

• Unnamed Item
• Numerical continuation methods for studying periodic travelling wave (wavetrain) solutions of partial differential equations
• Newton-Krylov continuation of periodic orbits for Navier-Stokes flows
• Snakes and ladders: localized states in the Swift-Hohenberg equation
• Nonequilateral hexagonal patterns
• Pattern formation on the free surface of a ferrofluid: spatial dynamics and homoclinic bifurcation
• Hexagonal patterns in finite domains
• Snaking branches of planar BCC fronts in the 3D Brusselator
• Phyllotaxis: some progress, but a story far from over
• Computing absolute and essential spectra using continuation
• On localised hotspots of an urban crime model
• Numerical continuation methods for dynamical systems. Path following and boundary value problems.
• Pattern formation in the presence of symmetries
• Homoclinic snaking near the surface instability of a polarisable fluid
• Continuation and Bifurcation of Grain Boundaries in the Swift--Hohenberg Equation
• Localized Patterns in Periodically Forced Systems: II. Patterns with Nonzero Wavenumber
• Characterizing the Effect of Boundary Conditions on Striped Phases
• Pattern Formation
• Localized Hexagon Patterns of the Planar Swift–Hohenberg Equation
• Localized Hexagonal Patterns
• Homoclinic snaking: Structure and stability
• SHAPE AND SIZE EFFECTS IN LOCALIZED HEXAGONAL PATTERNS
• A Storage-Efficient $WY$ Representation for Products of Householder Transformations
• A Sherman–Morrison–Woodbury Identity for Rank Augmenting Matrices with Application to Centering
• Solving Nonlinear Equations with Newton's Method
• Propagation of hexagonal patterns near onset
• Spectral Methods in MATLAB
• An Adaptation of Krylov Subspace Methods to Path Following Problems
• Invasion Fronts Outside the Homoclinic Snaking Region in the Planar Swift--Hohenberg Equation
• Three-dimensional doubly diffusive convectons: instability and transition to complex dynamics
• Growing Stripes, with and without Wrinkles
• Stationary Coexistence of Hexagons and Rolls via Rigorous Computations
• Fourth-Order Time-Stepping for Stiff PDEs
• Continuation of Localized Coherent Structures in Nonlocal Neural Field Equations
• PHASE INSTABILITIES OF DISTORTED HEXAGONAL PATTERNS

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