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Bifurcation from rolls to multi-pulse planforms via reduction to a parabolic Boussinesq model

Bridges, TJ (2014) Bifurcation from rolls to multi-pulse planforms via reduction to a parabolic Boussinesq model Physica D: Nonlinear Phenomena, 275. pp. 8-18.

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Abstract

A mechanism is presented for the bifurcation from one-dimensional spatially periodic patterns (rolls) into two-dimensional planar states (planforms). The novelty is twofold: the planforms are solutions of a Boussinesq partial differential equation (PDE) on a periodic background and secondly explicit formulas for the coefficients in the Boussinesq equation are derived, based on a form of planar conservation of wave action flux. The Boussinesq equation is integrable with a vast array of solutions, and an example of a new planform bifurcating from rolls, which appears to be generic, is presented. Adding in time leads to a new time-dependent PDE, which models the nonlinear behaviour emerging from a generalization of Eckhaus instability. The class of PDEs to which the theory applies is evolution equations whose steady part is a gradient elliptic PDE. Examples are the 2+1 Ginzburg-Landau equation with real coefficients, and the 2+1 planar Swift-Hohenberg equation. © 2014 Elsevier B.V. All rights reserved.

Item Type: Article
Authors :
NameEmailORCID
Bridges, TJt.bridges@surrey.ac.ukUNSPECIFIED
Date : 1 May 2014
Identification Number : 10.1016/j.physd.2014.02.004
Depositing User : Symplectic Elements
Date Deposited : 17 May 2017 13:14
Last Modified : 17 May 2017 15:09
URI: http://epubs.surrey.ac.uk/id/eprint/838466

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