Optical soliton solutions of the stochastic perturbed Radhakrishnan-Kundu-Lakshmanan equation via Itô Calculus

Abstract

Abstract This study presents, for the first time, optical solitons of the stochastic perturbed Radhakrishnan-Kundu-Lakshmanan equation with Kerr law nonlinearity in the presence of chromatic and spatio-temporal dispersions. The stochastic form involves multiplicative white noise in the Ito sense, besides; the Kudryashov and the new Kudryashov methods are picked to analyze. The analysis of the stochastic soliton solutions of the Radhakrishnan-Kundu-Lakshmanan equation and the impact of noise on these solitons are the primary motivations for choosing both of these techniques rather than obtaining many solitons. Therefore, the first goal is to obtain the most basic soliton types, bright and dark solitons, and the second goal is to observe the white noise effect on these solitons. By applying the proposed methods, bright and dark solitons are obtained, and the noise effect on these solitons is illustrated using both 3D and 2D graphic presentations, along with necessary comments. The presentation of the examined model for the first time in this article reflects its originality in terms of contributing both the study and the obtained results to the literature.