Pulses in a complex Ginzburg-Landau system: Persistence under coupling with slow diffusion
The article studies existence and persistence of traveling pulse solutions for a complex Ginzburg-Landau equation coupled to a diffusion equation that acts on a long spatial scale (slow diffusion). The authors choose a model that forms a connection between two limiting systems of a very different nature: the diffusion equation is coupled with a real Ginzburg-Landau system on one hand (having dissipative dynamics), when the coefficients have small imaginary parts, and with a nonlinear Schrödinger equation on the other hand (which is Hamiltonian, integrable and with infinitely many conservation laws). In both cases existence and persistence results are proved, using analytical, partly asymptotic and geometric methods.
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