Rigorous Computation of a Radially Symmetric Localized Solution in a Ginzburg--Landau Problem

DOI10.1137/140987973zbMath1319.34048OpenAlexW2088602157MaRDI QIDQ5250034

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Publication date: 15 May 2015

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

Full work available at URL: https://semanticscholar.org/paper/3dc9ee9e578df9fb64a96640cd5c1a0f8ba0d91b

zbMATH Keywords

Ginzburg-Landau equationSwift-Hohenberg equationcomputer-assisted proofradial symmetrylocalized solutionnonautonomous ODE

Mathematics Subject Classification ID

Singular nonlinear boundary value problems for ordinary differential equations (34B16) Boundary value problems on infinite intervals for ordinary differential equations (34B40) Ginzburg-Landau equations (35Q56)

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Uses Software

• Mathematica
• Matlab
• INTLAB
• RODES

Cites Work

• Analytic estimates and rigorous continuation for equilibria of higher-dimensional PDEs
• Computer-assisted methods for the study of stationary solutions in dissipative systems, applied to the Kuramoto-Sivashinski equation
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• A rigorous ODE solver and Smale's 14th problem
• Boundary value problems for a class of nonlinear differential equations
• Rigorous numerics for analytic solutions of differential equations: the radii polynomial approach
• Spots in the Swift--Hohenberg Equation
• Rigorous Numerics for Symmetric Connecting Orbits: Even Homoclinics of the Gray–Scott Equation
• Validated Continuation for Equilibria of PDEs
• Localized radial solutions of the Swift–Hohenberg equation
• Chaotic Braided Solutions via Rigorous Numerics: Chaos in the Swift–Hohenberg Equation
• A computer-assisted proof of the Feigenbaum conjectures
• A Numerical Verification Method for Solutions of Boundary Value Problems with Local Uniqueness by Banach's Fixed-Point Theorem
• Radially symmetric patterns of reaction-diffusion systems
• Rigorous Computation of a Radially Symmetric Localized Solution in a Ginzburg--Landau Problem
• Stationary Coexistence of Hexagons and Rolls via Rigorous Computations
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