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Nearly real fronts in a Ginzburg–Landau equation

Published online by Cambridge University Press:  14 November 2011

Christopher K. R. T. Jones ,
Todd M. Kapitula  and
James A. Powell
Christopher K. R. T. Jones
Affiliation:
Department of Mathematics, University of Maryland, College Park, Maryland 20742, U.S.A.
Todd M. Kapitula
Affiliation:
Department of Mathematics, University of Maryland, College Park, Maryland 20742, U.S.A.
James A. Powell
Affiliation:
Department of Mathematics, University of Arizona, Tucson, Arizona 85721, U.S.A.
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Synopsis

Subcritical fronts are shown to exist in a quintic version of the well-known complex Ginzburg–Landau equation, which has a subcritical pitchfork as well as a supercritical saddle-node bifurcation. The fronts connect a finite amplitude plane wave state to a stable zero solution. The unstable manifold at finite amplitude and stable manifold of vanishing amplitude solutions are shown to intersect transversely on an invariant zero-wavenumber manifold with parameters set to be real. By the persistence of transverse intersection, frontal connections exist for a continuum of nearly real fronts parametrised by appropriate variables that exhibit some interesting changes in dimension.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 116 , Issue 3-4 , 1990 , pp. 193 - 206
Copyright
Copyright © Royal Society of Edinburgh 1990

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