Taming spatiotemporal chaos by impurities in the parametrically driven damped nonlinear schrodinger equation

Solitons of the parametrically driven, damped nonlinear Schrodinger equatio n become unstable and seed spatiotemporal chaos for sufficiently large driv ing amplitudes. We show that the chaos can be suppressed by introducing loc alized inhomogeneities in the parameters of the equation. The pinning of th e soliton on an "attractive" inhomogeneity expands its stability region whe reas "repulsive" impurities produce an effective partitioning of the interv al. We also show that attractive impurities may spontaneously nucleate soli tons which subsequently remain pinned on these defects. A brief account of these results has appeared in patt-so1/9906001, where the interested reader can also find multicolor versions of the figures.