Alshammari Fahad Sameer, Roshid Harun-Or-, Asif Md, Hoque Md Fazlul, Aldurayhim Abdullah
Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam bin Abdulaziz University, Alkharj, 11942, Saudi Arabia.
Department of Mathematics, Pabna University of Science and Technology, Bangladesh.
Heliyon. 2023 May 23;9(6):e16570. doi: 10.1016/j.heliyon.2023.e16570. eCollection 2023 Jun.
This article explores on a stochastic couple models of ion sound as well as Langmuir surges propagation involving multiplicative noises. We concentrate on the analytical stochastic solutions including the travelling and solitary waves by using the planner dynamical systematic approach. To apply the method, First effort is to convert the system of equations into the ordinary differential form and present it in form of a dynamic structure. Next analyze the nature of the critical points of the system and obtain the phase portraits on various conditions of the corresponding parameters. The analytic solutions of the system in an account of distinct energy states for each phase orbit are performed. We also show how the results are highly effective and interesting to realize their exciting physical as well as the geometrical phenomena based on the demonstration of the stochastic system involving ion sound as well as Langmuir surges. Descriptions of effectiveness of the multiplicative noise on the obtained solutions of the model, and its corresponding figures are demonstrated numerically.
本文探讨了离子声的随机耦合模型以及涉及乘性噪声的朗缪尔波涌传播。我们通过使用平面动力系统方法专注于包括行波和孤立波在内的解析随机解。为应用该方法，首先要将方程组转化为常微分形式并以动态结构的形式呈现。接下来分析系统临界点的性质并获得对应参数各种条件下的相图。考虑每个相轨道不同能量状态对系统进行解析求解。我们还基于涉及离子声和朗缪尔波涌的随机系统的演示，展示了这些结果如何非常有效地且有趣地实现其令人兴奋的物理以及几何现象。数值展示了乘性噪声对模型所得解的有效性描述及其相应图形。
