The \(1:\sqrt 2\) Hopf/steady-state mode interaction in three-dimensional magnetoconvection

DOI10.1016/S0167-2789(99)00210-9zbMath0942.35141OpenAlexW2076859374MaRDI QIDQ1972889

Jonathan H. P. Dawes

Publication date: 28 August 2000

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0167-2789(99)00210-9

zbMATH Keywords

normal formmode interaction3D magnetoconvectiondrifting solutionsdynamics near onset

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Magnetohydrodynamics and electrohydrodynamics (76W05) Bifurcations in context of PDEs (35B32) Normal forms, center manifold theory, bifurcation theory for infinite-dimensional dissipative dynamical systems (37L10)

Related Items (4)

The \(1:\sqrt 2\) mode interaction and heteroclinic networks in Boussinesq convection ⋮ Spatial period-multiplying instabilities of hexagonal Faraday waves ⋮ The 1 : 2 spatial resonance on a hexagonal lattice in two-layered Rayleigh–Bénard problems ⋮ Necessary conditions for the existence of quasi-polynomial invariants: the quasi-polynomial and Lotka-Volterra systems

Uses Software

• AUTO

Cites Work

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• Bifurcation from relative periodic solutions
• The Takens-Bogdanov bifurcation with O(2)-symmetry
• The interaction of two spatially resonant patterns in thermal convection. Part 1. Exact 1:2 resonance
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• Steady-state mode interactions in the presence of 0(2)-symmetry
• Stability results for steady, spatially periodic planforms
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• Travelling and standing waves in magnetoconvection
• A PSEUDOSPECTRAL CODE FOR CONVECTION WITH AN ANALYTICAL/NUMERICAL IMPLEMENTATION OF HORIZONTAL BOUNDARY CONDITIONS
• Compressible magnetoconvection in three dimensions: planforms and nonlinear behaviour

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