Fundamental solutions to the stochastic perturbed nonlinear Schrödinger’s equation via gamma distribution

Abstract

We introduce a new stochastic robust solver to solve several classes of nonlinear stochastic partial differential equations (NSPDEs). This solver presents the closed formula for the stochastic solutions. In this regard, this solver is developed to accurately present the complete wave structure of the NSPDEs. To verify this solver, an application is given. The acquired stochastic solutions may be applicable for some new observations in superfluid, new physics, engineering and biology. The theoretical study shows that the proposed solver is sturdy and efficacious. The obtained stochastic optical soliton solutions are presented graphically to clarify their physical parameters. Moreover, the constraint conditions are utilized to verify the existence solutions. In the view of the characterization for the behavior of random solutions utilizing their statistical features, the expectation and variance values of these solutions are considered.

Keywords

• 34A34
• 35C08
• 35Q62
• 35Q80