Bright and Dark solitary Wave Solution for Higher Order NLS equation with cubic and quintic Effects

Abstract

Using the coupled amplitude phase technique, we find general analytical bright solitary wave solution for the higher order nonlinear Schrudinger equation with cubic-quintic terms which describes the effects of femto-second optical soliton pulse propagation in the non-Kerr medium. Also, we find the analytical dark soliton solution by Jacobin elliptical function.