Geometric Brownian motion

Motion (physics)

Statistics

Brownian motion

Physics

Signal transfer function

Analog signal

Mathematical analysis

Nonlinear system

Trigonometric functions

Multiplicative noise

Geometry

Applied mathematics

Trigonometry

Innovation diffusion

Mathematics

Mathematical physics

Computer science

Multiplicative function

Knowledge management

Quantum mechanics

Diffusion process

Classical mechanics

Digital signal processing

Computer hardware

Symmetry

In this article, the stochastic Davey–Stewartson equations (SDSEs) forced by multiplicative noise are addressed. We use the mapping method to find new rational, elliptic, hyperbolic and trigonometric functions. In addition, we generalize some previously obtained results. Due to the significance of the Davey–Stewartson equations in plasma physics, nonlinear optics, hydrodynamics and other fields, the discovered solutions are useful in explaining a number of intriguing physical phenomena. By using MATLAB tools to simulate our results and display some of 3D graphs, we show how the multiplicative Brownian motion impacts the analytical solutions of the SDSEs. Finally, we demonstrate the effect of multiplicative Brownian motion on the stability and the symmetry of the achieved solutions of the SDSEs.

Multiplicative Brownian Motion Stabilizes the Exact Stochastic Solutions of the Davey–Stewartson Equations