Construction of exact solutions for a higher-order stochastic modified Gerdjikov–Ivanov model using the IMETF method

Abstract The multiplicative white noise in the Ito interpretation is included for the first time in the perturbed higher-order modified Gerdjikov–Ivanov (HMGI) equation, that is considered the focus of the current study. In this work, we investigate the suggested model using the improved modified extended tanh-function (IMETF) method with the goal of producing brilliant and unique solitons such as dark and bright solitons, singular and singular periodic solutions, hyperbolic wave solutions, Weierstrass elliptic doubly periodic solutions, rational, exponential function solutions and Jacobi elliptic functions (JEFs). These extracted solutions demonstrate the effectiveness and potency of the used methodology. The used method specifies our research objective, which is related to solitons. These obtained soliton solutions are useful resources for examining a range of phenomena when there is white noise present. We examine how various wave phenomena are affected by noise, with a special emphasis on soliton solutions. Our findings indicate that the phase component for the obtained solitons of the suggested governing model is the primary goal of the white noise. This study is the first to show the optical soliton solutions derived from the perturbed HMGI equation under multiplicative white noise influence. The contribution of our work is the application of this phenomenon to a model equation in a new context that neither has been studied nor discovered before for optical soliton solutions. With the derived findings, our knowledge of wave events in nonlinear optical systems has advanced significantly.