Optical soliton perturbation of the Gerdjikov–Ivanov equation with spatio-temporal dispersion using a modified extended direct algebraic method

Abstract

Our paper investigates the optical solitons with the Gerdjikov–Ivanov equation having spatio-temporal dispersion. The modified extended direct algebraic algorithm is implemented to extract solitons and other types of solutions for this model. Bright, dark and singular soliton solutions are retrieved with their constraints for the validity of these solitons. Additionally, different structures of solutions are listed. Furthermore, some selected solitons are illustrated graphically.