Stochastic soliton solutions of ion sound and Langmuir wave equation via new extended direct algebraic method with bifurcation and modulation instability analyses

This paper investigates the impact of multiplicative noise on the stochastic equations of ion sound and Langmuir waves in the Itô sense. The stochastic soliton solutions of the stochastic equations of the ion sound and Langmuir waves are obtained by employing the new extended direct algebraic method. It further examines the system’s stability characteristics through bifurcation and modulation instability analyses. Due to the inherently random and unpredictable nature of plasma environments, incorporating noise effects is vital for accurately capturing energy transport and localization phenomena. The new extended direct algebraic method enables the systematic construction of stochastic solitons, stochastic periodic waves, and other localized stochastic solutions. The results demonstrate that the extended direct algebraic method effectively handles the complexity introduced by stochastic terms, revealing exact soliton solutions and highlighting the significant role of stochastic parameters in plasma dynamics through the emergence of noise-modulated localized structures. The novelty of this work lies in the first application of the new extended direct algebraic method to a stochastic plasma model, offering new physical insights into the nonlinear dynamics of Langmuir and ion sound waves under noise effects.