This paper recovers optical solitons to the newly proposed dispersive concatenation model that comes with power law of self-phase modulation. The presence of white noise in the Itô sence makes the model stochastic. Two integration approaches retrieve bright and singular optical solitons. The intermediary Weierstrass ’ elliptic functions are implemented for this retrieval. It has been established that the effect of white noise stays confined to the phase component of the solitons.