Abstract
This paper carries out the integration of the nonlinear dispersive Schrodinger equation with generalized evolution by the aid of Lie symmetry analysis. We study three types of nonlinearity in this paper. These are power law nonlinearity, dual-power law nonlinearity, and finally log law nonlinearity. From the first two types of nonlinearity the special cases of the Kerr law and parabolic law nonlinearity are easily revealed.