Fluid dynamical form of the linear and nonlinear Schrödinger equations

The Hamiltonian theory of perfect fluids admits the generalization to cases where the internal energy density depends on the gradient of mass density. Though the fluid dynamical equations are not greatly modified, when they are transformed into wave equations, special cases of the generalized fluid are seen to correspond to familiar Schrödinger equations. The irrotational nonrelativistic case is presented here and some of the advantages of the fluid point of view are mentioned.