Lie Symmetry Analysis of the Nonlinear Schrödinger Equation with Time Dependent Variable Coefficients

Abstract

In this work, we study the generalized nonlinear Schrodinger equation having time dependent variable coefficients by using Lie group method. We find the Lie point symmetries admitted by the Schrodinger equation for arbitrary variable coefficients and from the obtained symmetries, we constructed the similarity reductions. As the further symmetry analysis of the reduced ordinary differential equations was not possible due to lack of symmetries, we, therefore, solve one of the reduced nonlinear ordinary differential equation for completeness by using power series method and presented the exact series solution. The convergence of the series solutions is also established.