New optical stochastic solutions for the Schrödinger equation with multiplicative Wiener process/random variable coefficients using two different methods

Abstract

In this article, we take into consideration the stochastic Schrödinger equation (SSE) perturbed in the Itô sense by the multiplicative Wiener process. We employ an appropriate transformation to turn the SSE into another Schrödinger equation with random variable coefficients (SE-RVCs). We used the generalizing Riccati equation mapping method and the Jacobi elliptic function method to find novel hyperbolic, trigonometric, rational, and elliptic functions solutions for SE-RVCs. After that, we can acquire the SSE solutions. For the first time, in this work, we assume that the solution to the wave equation for the Schrödinger equation is stochastic, whereas all earlier studies assumed it to be deterministic. Furthermore, we give various graphs to display the effect of multiplicative Wiener process on the exact solutions to the SSE. We deduce that the multiplicative Wiener process stabilizes the solutions of the SSE.

Keywords

• random variable coefficients
• schrödinger equation
• stability by noise
• generalizing riccati equation mapping method