Vv. Afanasjev et N. Akhmediev, A NEW KIND OF PERIODIC STATIONARY SOLUTION OF THE CUBIC GINZBURG-LANDAU EQUATION, Physica. A, 233(3-4), 1996, pp. 801-808
We analyze the long-scale dynamics of the modulationally unstable plan
e wave in the cubic complex Ginzburg-Landau equation without a diffusi
on term. Our numerical studies reveal that when the dissipative effect
s dominate over the conservative effects a new kind of temporally stat
ionary but spatially periodic solution can be found.