Multistable Pulse-like Solutions in a Parametrically Driven Ginzburg-Landau Equation

Abstract

It is well known that pulse-like solutions of the cubic complex Ginzburg-Landau equation are unstable but can be stabilised by the addition of quintic terms. In this paper we explore an alternative mechanism where the role of the stabilising 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.

13 pages, 6 figures; to appear in PRE

References in corpus (4)

• The World of the Complex Ginzburg-Landau Equation
• Parametrically Driven Dark Solitons
• Soliton-radiation coupling in the parametrically driven, damped nonlinear Schrödinger equation
• Solitary pulses and periodic waves in the parametrically driven complex Ginzburg-Landau equation

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• A quasi-periodic route to chaos in a parametrically driven nonlinear medium
• Dissipative structures in a parametrically driven dissipative lattice: chimera, localized disorder, continuous-wave, and staggered state
• Boundary effects on localized structures in spatially extended systems
• Breather bound states in a parametrically driven magnetic wire
• Solitons in a parametrically driven damped discrete nonlinear Schrödinger equation