  We study spatio-temporal chaos in the complex Ginzburg-Landau equation in
parameter regions of weak amplification and viscosity. Turbulent states
involving many soliton-like pulses appear in the parameter range, because the
complex Ginzburg-Landau equation is close to the nonlinear Schr\"odinger
equation. We find that the distributions of amplitude and wavenumber of pulses
depend only on the ratio of the two parameters of the amplification and the
viscosity. This implies that a one-parameter family of soliton turbulence
states characterized by different distributions of the soliton parameters
exists continuously around the completely integrable system.
