Bifurcation and Analytical Solutions of the Space-Fractional Stochastic Schrödinger Equation with White Noise

Abstract

The qualitative theory for planar dynamical systems is used to study the bifurcation of the wave solutions for the space-fractional nonlinear Schrödinger equation with multiplicative white noise. Employing the first integral, we introduce some new wave solutions, assorted into periodic, solitary, and kink wave solutions. The dependence of the solutions on the initial conditions is investigated. Some solutions are clarified by the display of their 2D and 3D representations with varying levels of noise to show the influence of multiplicative white noise on the solutions.

Keywords

• stochastic shrödinger equation
• dynamical systems
• white noise
• bifurcation analysis
• phase space
• fractional derivatives