Radial amplitude equations for fully localized planar patterns

DOI10.1137/24M1644298MaRDI QIDQ6660877

Dan J. Hill, David J. B. Lloyd

Publication date: 10 January 2025

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

zbMATH Keywords

asymptotic analysisamplitude equationslocalized patterns

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Reaction-diffusion equations (35K57) Nonlinear elliptic equations (35J60) Bifurcations in context of PDEs (35B32) Multiple scale methods for ordinary differential equations (34E13) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Ginzburg-Landau equations (35Q56)

Cites Work

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• Error estimates for the Ginzburg-Landau approximation
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• Pattern Formation
• Localized radial solutions of the Swift–Hohenberg equation
• Localized Hexagon Patterns of the Planar Swift–Hohenberg Equation
• Radially symmetric patterns of reaction-diffusion systems
• Phase dynamics in the real Ginzburg-Landau equation
• Propagation of hexagonal patterns near onset
• The Validity of Generalized Ginzburg-Landau Equations
• Existence of localized radial patterns in a model for dryland vegetation
• Spatially localized structures in dissipative systems: open problems
• Patterns and Quasipatterns from the Superposition of Two Hexagonal Lattices
• Approximate localised dihedral patterns near a turing instability
• Dihedral rings of patterns emerging from a Turing bifurcation

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