On the Group Theoretic Approach to the Symmetries for a Class of Generalized Nonlinear Schrodinger Equation, iψt - ψxx = f(x, ψ, ψ*, ψx, ψx*)

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Abstract
We have analysed in detail the Lie type symmetries for a class of non-linear Schrödinger equation iψt - ψxx = f(x, ψ, ψ*, ψx, ψx*) where the nonlinear part may depend both on ψ, ψx and explicitly on x. This class also encompasses the new type of NLSE discovered by Ichikawa and others. In each case the relevant transformations are obtained and the corresponding differential equations are deduced. It is observed that the general structure of the infinitesimals for the whole class has a unique dependence on ψ, ψ* and is governed to a large extent by the linear part while the structure of nonlinearity introduces, finer details to the functions involved in the transformation. Our comparative study of six equations belonging to a given class of NLSE reveals this in detail. Lastly we deduce the ordinary differential equations belonging to those equations.

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