Optical envelope patterns perturbation with full nonlinearity for Gerdjikov–Ivanov equation by trial equation method

Abstract In this paper, the classification of all envelope traveling wave solutions of Gerdjikov–Ivanov model with full nonlinearity is obtained by using complete discriminant system for polynomial method and trial equation method. All the results show that the Gerdjikov–Ivanov model has abundant traveling wave solutions, including isolated solutions, periodic solutions, rational singular solutions, double periodic continuous solutions and discontinuous solutions. Among them, some new solutions are obtained.