A method to solve nonlinear Schrödinger equation using Riccati equation

Abstract: A method to find exact solutions to nonlinear Schr\"odinger equation, defined on a line and on a plane, is found by connecting it with second order linear ordinary differential equation. The connection is essentially made using Riccati equation. Generalisation of several known solutions is found using this method, in case of nonlinear Schr\"odinger equation defined on a line. This method also yields non-singular and singular vortex solutions, when applied to nonlinear Schr\"odinger equation on a plane.