Madani Yasir A, Hussain Shabbir, Almalahi Mohammed A, Muflh Blgys, Aldwoah Khaled A, Abdalla Mukhtar Y Y
Department of Mathematics, College of Science, University of Ha'il, Ha'il, 2440, Saudi Arabia.
Department of Mathematics and Statistics, University of Lahore, Lahore, Pakistan.
Sci Rep. 2025 May 25;15(1):18169. doi: 10.1038/s41598-025-03237-8.
This article investigates the stochastic Davey-Stewartson equations influenced by multiplicative noise within the framework of the Itô calculus. These equations are of significant importance because they extend the nonlinear Schrödinger equation into higher dimensions, serving as fundamental models for nonlinear phenomena in plasma physics, nonlinear optics, and hydrodynamics. This paper is motivated by the need to understand how random fluctuations affect soliton behavior in nonlinear systems. This is particularly relevant in applications such as turbulent plasma waves and optical fibers, where noise can significantly impact wave propagation. We employ the modified extended direct algebraic method for finding exact stochastic soliton solutions to the stochastic Davey-Stewartson equations. The study derives a class of exact stochastic soliton solutions, including dark, singular, rational, and periodic waves. MATLAB is used to provide visual representations of these stochastic soliton solutions through 3D surface plots, contour plots, and line plots. These solutions offer essential insights into how random disturbances influence nonlinear wave systems, particularly in turbulent plasma waves and optical fibers. To the best of our knowledge, the application of the modified extended direct algebraic method to the stochastic Davey-Stewartson equations with multiplicative noise, along with the subsequent analysis of the stabilizing effects on dark, singular, rational, and periodic stochastic soliton solutions is novel. The study demonstrates how multiplicative Brownian motion regulates these wave structures, providing new information on the impact of noise on higher-dimensional nonlinear systems.
本文在伊藤微积分框架下研究了受乘性噪声影响的随机戴维 - 斯图尔特森方程。这些方程具有重要意义，因为它们将非线性薛定谔方程扩展到了更高维度，是等离子体物理学、非线性光学和流体动力学中非线性现象的基本模型。本文的动机在于理解随机涨落在非线性系统中如何影响孤子行为。这在诸如湍流等离子体波和光纤等应用中尤为相关，在这些应用中噪声会显著影响波的传播。我们采用改进的扩展直接代数方法来求解随机戴维 - 斯图尔特森方程的精确随机孤子解。该研究推导得出了一类精确的随机孤子解，包括暗波、奇异波、有理波和周期波。利用MATLAB通过三维表面图、等高线图和线图对这些随机孤子解进行可视化表示。这些解为随机扰动如何影响非线性波系统提供了重要见解，特别是在湍流等离子体波和光纤方面。据我们所知，将改进的扩展直接代数方法应用于具有乘性噪声的随机戴维 - 斯图尔特森方程，并随后对暗、奇异、有理和周期随机孤子解的稳定效应进行分析是新颖的。该研究展示了乘性布朗运动如何调节这些波结构，为噪声对高维非线性系统的影响提供了新的信息。
