Exploring novel applications of stochastic differential equations: Unraveling dynamics in plasma physics with the Tanh-Coth method

This study addresses the solution of differential equations converted into stochastic differential equations with the introduction of a noise term. To simplify the stochastic complexity, we employ a transformation, converting the equations into ordinary differential equations. The well-established Tanh-Coth method is then applied for analytical solutions to the resulting ordinary differential equations. Graphical representations of the solutions are presented, providing insights into the system's dynamics. The proposed methodology offers a robust approach to tackle the challenges posed by stochasticity in differential equations. The Tanh-Coth method efficacy in handling nonlinearities is leveraged, contributing to the analytical solution. The graphical analysis enhances the interpretation of results, shedding light on the impact of stochastic components on the system's behavior. Overall, this study provides a valuable tool for researchers and practitioners dealing with stochastic processes, offering a concise yet comprehensive approach to understanding and solving differential equations in the presence of randomness. The study aims to address the complexity of stochasticity in differential equations by introducing a noise term and transforming them into ordinary differential equations for easier analysis. Leveraging the Tanh-Coth method, it provides analytical solutions to the transformed equations, offering insights into system dynamics through graphical representations. Ultimately, the study aims to offer a robust approach to tackle stochastic processes in differential equations, benefiting researchers and practitioners dealing with stochastic phenomena.