Objective: This article studies optical solitons with nonlinear Schrödinger's equation having a new form of self-phase modulation as proposed by Kudryashov in presence of multiplicative white noise for the first time. Methods: The new mapping method is applied to extract solitons with the newly structured model equation. The integration scheme yields a spectrum of individual and straddled solitons. The recovered solitons are enumerated after a quick revisitation of the model together with its modified version and the mathematical strategies. Results: Dark, bright and singular solitons with the model are retrieved using the mathematical approach. Such solitons are indicated with the help of the certain restrictions. Singular periodic solutions are also derived from the mathematical scheme. Conclusion: Optical solitons with the new model are retrieved in this work for the first time. The white noise appears only in the soliton phase component and the wave-number is therefore stochastic. The amplitude and speed of the soliton do not get affected with the presence of multiplicative white noise. The current model being fairly new has a lot of openings that would lead to an abundance of new results which are yet to be ventured.
- Itô Calculus
- White noise