Invariance of the nonlinear generalized NLS equation under the Lie group of scaling transformations

The nonlinear generalized NLS equation in the sense of the Riemann–Liouville derivatives is considered. The symmetry properties of nonlinear generalized NLS equation is investigated by using the Lie group analysis method. By right of the obtained Lie point symmetries, it is shown that this equation could transform into a nonlinear ordinary differential equation of fractional order with the new independent variable. The derivative is an Erdélyi–Kober derivative depending on a parameter α .