Multiple Elliptic, Hyperbolic and Trigonometric Stochastic Solutions- for the Stochastic Coupled Schrödinger-KdV Equations in Dusty Plasma (Contemporary Mathematics, 2025)
In this paper, we consider the stochastic coupled Schrödinger-KdV equations forced by multiplicative Brownian motion in the Itô sense. By using a mapping method, we can obtain abundant elliptic, trigonometric, and hyperbolic stochastic solutions. The obtained results show that this method is an effective mathematical tool for finding analytical solutions to our equation. In the absence of noise, we get some previously solutions of the coupled Schrödinger-KdV equations. Because the coupled Schrödinger-KdV equations have significant applications in dusty plasma, including Langmuir, electromagnetic waves, and dust-acoustic waves, these derived solutions may be used to analyze a wide range of essential physical phenomena. Moreover, the impacts of the noise term on the analytical solution of the stochastic coupled Schrödinger-KdV equations were demonstrated. We conclude that the multiplicative Brownian motion stabilizes the solutions to the stochastic coupled Schrödinger-KdV equations.
Keywords: analytical solutions; stochastic process; brownian motion; mapping method; noise strength