Abstract
In this paper the perturbed nonlinear Schrödinger equation (PNLSE) with power law nonlinearity in the medium of non-kerr is analyzed by employing Reccati equation mapping method. Perturbed nonlinear Schrödinger equation depict the effect of quantic non-linearity on propagation of the ultra-short optical pulses in the medium of non-kerr, similar to optical fibers. We achieved various types of soliton solutions, some of them are novel and does not exist previously. Graphical presentation of some obtained exact solutions are also given through assigning suitable values to the parameters that aids to understand the physical phenomenon of this models. Modulation Instability (MI) is also discussed by standard linear-stability analysis that shows about all achieved results are exact and stable. The computational exertion and achieved outputs shows that the current proposed technique is powerful and effectual. Furthermore many higher order non-linear Schrödinger equations can be solved using current method.