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Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Nov;68(5 Pt 2):056605. Epub 2003 Nov 24.

Multistable pulselike solutions in a parametrically driven Ginzburg-Landau equation.

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  • 1Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch 7701, South Africa.


It is well known that pulselike solutions of the cubic complex Ginzburg-Landau equation are unstable but can be stabilized by the addition of quintic terms. In this paper we explore an alternative mechanism where the role of the stabilizing agent is played by the parametric driver. Our analysis is based on the numerical continuation of solutions in one of the parameters of the Ginzburg-Landau equation (the diffusion coefficient c), starting from the nonlinear Schrödinger limit (for which c=0). The continuation generates, recursively, a sequence of coexisting stable solutions with increasing number of humps. The sequence "converges" to a long pulse which can be interpreted as a bound state of two fronts with opposite polarities.

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