Exact solutions of the inhomogeneous nonlinear Schr\"odinger equation through supersymmetric potentials

Abstract

By employing supersymmetric quantum mechanics, we present a general algorithm to construct supersymmetric partner potentials and hence derive exact stationary solutions of the inhomogeneous nonlinear Schr\"odinger equation (INLSE). This is possible due to the connection between the INLSE and the nonlinear Schr\"odinger equation (NLSE), which can be established from a treatment based on Lie point symmetries and is related with Schr\"odinger equation, under certain conditions. As an illustrative example, we construct exact solutions for the INLSE through a P\"osch-Teller potential with a single bound state.