Nonlinear Sciences – Pattern Formation and Solitons
Scientific paper
1996-09-13
Nonlinear Sciences
Pattern Formation and Solitons
16 pages (latex) including 11 figures; accepted for publication in Physica D
Scientific paper
10.1016/S0167-2789(96)00211-4
We consider domain walls (DW's) between single-mode and bimodal states that occur in coupled nonlinear diffusion (NLD), real Ginzburg-Landau (RGL), and complex Ginzburg-Landau (CGL) equations with a spatially dependent coupling coefficient. Group-velocity terms are added to the NLD and RGL equations, which breaks the variational structure of these models. In the simplest case of two coupled NLD equations, we reduce the description of stationary configurations to a single second-order ordinary differential equation. We demonstrate analytically that a necessary condition for existence of a stationary DW is that the group-velocity must be below a certain threshold value. Above this threshold, dynamical behavior sets in, which we consider in detail. In the CGL equations, the DW may generate spatio-temporal chaos, depending on the nonlinear dispersion.
Hecke Martin van
Malomed Boris A.
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