Tests of Integrability of the Supersymmetric Nonlinear Schrodinger Equation

Abstract

We apply various conventional tests of integrability to the supersymmetric nonlinear Schrödinger equation. We find that a matrix Lax pair exists and that the system has the Painlevé property only for a particular choice of the free parameters of the theory. We also show that the second Hamiltonian structure generalizes to superspace only for these values of the parameters. We are unable to construct a zero curvature formulation of the equations based on OSp(2$|$1). However, this attempt yields a nonsupersymmetric fermionic generalization of the nonlinear Schrödinger equation which appears to possess the Painlevé property.