Nonlinear Schr\"odinger equations from prequantum classical statistical   field theory
  We derive some important features of the standard quantum mechanics from a certain classical-like model -- prequantum classical statistical field theory, PCSFT. In this approach correspondence between classical and quantum quantities is established through asymptotic expansions. PCSFT induces not only linear Schr\"odinger's equation, but also its {\it nonlinear generalizations.} This coupling with ``nonlinear wave mechanics'' is used to evaluate the small parameter of PCSFT. 
Andrei Khrennikov