Ginsburg-Pitaevski-Gross differential equation with the Rosen-Morse and modified Woods-Saxon potentials

In this paper, we consider non-linear Ginsburg-Pitaevski- Gross equation with the Rosen-Morse and modi ed Woods-Saxon potentials which is corresponding to the quantum vortices and has important applications in turbulence theory. We use the Runge- Kutta-Fehlberg approximation method to solve the resulting non- linear equation.