Supplementary optical solitonic expressions for Gerdjikov–Ivanov equations with three Kudryashov-based methods

Abstract The present manuscript uses three Kudryashov-based methods to analytically inspect the class of Gerdjikov–Ivanov equations, which comprises the standard Gerdjikov–Ivanov equation and the perturbed Gerdjikov–Ivanov equation. Various optical solitonic solutions have been constructed. Certainly, as the reported solitonic structures happened to be exponential functions, diverse true solitonic solutions can easily be resorted to upon suitably fixing the involving parameters, including mainly the bright and singular solitons. Lastly, the study graphically examined some of the constructed structures, which were then found to portray some interesting known shapes in the theory of solitary waves and nonlinear Schrödinger equations. Additionally, the Kudryashov-index d has been noted to play a significant role in the propagation of complex waves in the nonlinear media described by Gerdjikov–Ivanov equations.