ON THE FLUID APPROXIMATION TO A NONLINEAR SCHRODINGER-EQUATION

We present a heuristic proof that the nonlinear Schrodinger equation ( NLS) -i partial derivative PSI/partial derivative t = 1/2 DELTA PSI 1/2(1 - Absolute value of PSI 2)PSI in 2 + 1 dimensions has a family o f solutions which can be well approximated by a collection of point vo rtices for a planar incompressible fluid. The novelty of our approach is that we begin with a representation of the NLS as a compressible pe rturbation of Euler's equations for hydrodynamics.