In this paper, we introduce a coupled system of the stochastic Radhakrishnan-Kundu-Lakshmanan equation in magneto-optic waveguides for the first time. Power law nonlinearity and multiplicative white noise in the Itô sense are incorporated into the system. The two integration algorithms used are the extended simplest equation approach and the improved Kudryashov’s approach. This study uses computer algebra systems to present dark, bright, and singular solitons.