  We consider a factorization of the non-stationary Schrodinger operator based
on the parabolic Dirac operator introduced by Cerejeiras/ Kahler/ Sommen. Based
on the fundamental solution for the parabolic Dirac operators, we shall
construct appropriated Teodorescu and Cauchy-Bitsadze operators. Afterwards we
will describe how to solve the nonlinear Schrodinger equation using Banach
fixed point theorem.
