Quasi-one-dimensional solutions and their interaction with two-dimensional dissipative solitons

Orazio Descalzi, Helmut R. Brand

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14 Scopus citations

Abstract

We describe the stable existence of quasi-one-dimensional solutions of the two-dimensional cubic-quintic complex Ginzburg-Landau equation for a large range of the bifurcation parameter. By quasi-one-dimensional (quasi-1D) in the present context, we mean solutions of fixed shape in one spatial dimension that are simultaneously fully extended and space filling in a second direction. This class of stable solutions arises for parameter values for which simultaneously other classes of solutions are at least locally stable: the zero solution, 2D fixed shape dissipative solitons, or 2D azimuthally symmetric or asymmetric exploding dissipative solitons. We show that quasi-1D solutions can form stable compound states with 2D stationary dissipative solitons or with azimuthally symmetric exploding dissipative solitons. In addition, we find stable breathing quasi-1D solutions near the transition to collapse. The analogy of several features of the work presented here to recent experimental results on convection by Miranda and Burguete is elucidated.

Original languageEnglish
Article number022915
JournalPhysical Review E
Volume87
Issue number2
DOIs
StatePublished - 26 Feb 2013

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