Symmetries and conservation laws of a new nonlinear Schrِdinger model

We consider a nonlinear canonical Schrِdinger model recently proposed by us, describing collectively interacting nonrelativistic particles via a generalized Exclusion-Inclusion Principle. Starting from the energy-momentum tensor we study the space-time symmetries of this model and derive the conserved quantities and the associated fluxes. We also study the influence of the Exclusion-Inclusion Principle on the discrete symmetries P and T as well as and on the Galileo and the conformal ones. Finally, we discuss a particular scale transformation related to the Exclusion-Inclusion Principle.