FROM DARK SOLITONS IN THE DEFOCUSING NONLINEAR SCHRODINGER TO HOLES IN THE COMPLEX GINZBURG-LANDAU EQUATION

Perturbation approaches developed so far for the dark soliton solutions of the (fully integrable) defocusing nonlinear Schrodinger equation cannot describe important aspects of the dynamics resulting from dissipative perturbations of the Ginzburg-Landau type. The reason is that spatially slowly decaying changes of the background wavenumber occur, which requires the use of matching technics. We show how the perturbation selects a 1 or 2-parameter subfamily from the 3-parameter family of dark solitons of the nonlinear Schrodinger equation. The dynamics of the perturbed system can then be described analytically as motion within this selected subfamily yielding interesting scenarios. Interaction with shocks occurring in the complex Ginzburg-Landau equation can be included in a straightforward way.