Nonlinear Schrödinger equations within the Nelson quantization pictures

We present a class of nonlinear Schr6dinger equations (NLSES) describing, in the mean field approximation, systems of interacting particles. This class of NLSES is obtained generalizing expediently the approach proposed in [G. K., Phys. Rev. A 55, 941 (199711, where a classical system obeying to an exclusion-inclusion principle is quantized using the Nelson stochastic quantization. The new class of NLSEs is obtained starting from the most geneml nonlinear classical kinetics compatible with a constant diffusion coefficient D = h/2m. Finally, in the case of s-stationary states, we propose a transformation which linearizes the NLSEs here proposed.