  A new nonlinear Schroedinger equation is obtained explicitly from the fractal
Brownian motion of a massive particle with a complex-valued diffusion constant.
Real-valued energy (momentum) plane wave and soliton solutions are found in the
free particle case. The hydro-dynamical model analog yields another (new)
nonlinear QM wave equation with physically meaningful soliton solutions. One
remarkable feature of this nonlinear Schroedinger equation based on a fractal
Brownian motion model, over all the other nonlinear QM models, is that the
quantum-mechanical energy functional coincides with the field theory one.
