2014•arXiv (Cornell University)Open access

A method to solve nonlinear Schrödinger equation using Riccati equation

Vivek M. Vyas, R. Gupta, C.N. Kumar, Prasanta K. Panigrahi

Abstract

A method to find exact solutions to nonlinear Schrödinger 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 Schrödinger equation defined on a line. This method also yields non-singular and singular vortex solutions, when applied to nonlinear Schrödinger equation on a plane.

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Key concepts: Riccati equation, Nonlinear Schrödinger equation, Mathematics, Algebraic Riccati equation, Nonlinear system, Mathematical analysis, Ordinary differential equation, Schrödinger equation