Exact solutions for the system of stochastic equations for the ion sound and Langmuir waves

Abstract

We consider the system of stochastic equations of the ion sound and Langmuir waves with multiplicative noise in the Itô sense. To get new exact stochastic solutions, we apply three distinct methods such as: He’s semi-inverse method, the Riccati–Bernoulli sub-ODE method and the sine–cosine method. Such solutions are crucial to understanding some exciting complicated physical phenomena. Also, we improve and generalize some previously obtained results. Moreover, we study the influence of multiplicative noise on the obtained solutions of the system of stochastic equations for the ion sound and Langmuir waves.