Dissipative Soliton — Complex Ginzburg-Landau

∂_tA = A + (1+ib)∂²_xA − (1+ic)|A|²A | Stable localized structures in dissipative nonlinear media

Dispersion b 0.5

Nonlinear phase c 2.0

Drive amplitude 1.0

Phase Diagram

Computing...

Benjamin-Feir instability:
1 + bc < 0 → unstable plane wave

|A(x,t)| shown in blue.
Phase arg(A) shown in orange.
CGL on periodic domain L=64.