Abstract
In this work, soliton solutions of higher order non-linear Schrödinger equation (NLSE) with derivative non-Kerr non-linear terms are constructed by employing two analytical techniques, namely, exp(-Φ(ζ))-expansion and improved simple equation methods. This dynamical model plays a key role in engineering and physics, and it can be equation of pulses promulgation behind ultra-short range in the system of optical communication. The constructed soliton solution helps researchers for understanding the physical phenomenon of this equation. The standard linear stability analysis is utilized and the stability of model is investigated which substantiate that all results are stable and exact. Graphically, the movements of some solutions are depicted at appropriate values of parameters. The achieved results shows simplicity, reliability and power of the current schemes.