Double reduction via invariance & conservation laws and analysis of solitons of the Gerdjikov–Ivanov equation in optics

Abstract We will study of the perturbed Gerdjikov–Ivanov equation, also known as derivative nonlinear Schrödinger-III. The dark soliton solutions are constructed analytically using some Ansatz method. Their physical aspects are discussed in this study for better understanding the behaviour of dark solitons with respect to different wave numbers. The invariance analysis will be carried out, conservation laws of DNLS-III will be constructed and presented and double reduction will used to find invariant solutions.