@article{Obeidat2025, 
author = {Sofian T. Obeidat and Doaa Rizk and Wael W. Mohammed},
title = {Exploration traveling solitary solutions to the modified Korteweg-de Vries equation with advection noise},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {11},
pages = {26334-26350},
keywords = {stochastic solutions, simulation, mathematical model, exact solutions, analytical techniques, noise intensity},
url = {https://www.sciopen.com/article/10.3934/math.20251158},
doi = {10.3934/math.20251158},
abstract = {In this study, we investigate the stochastic modified Korteweg-de Vries (SmKdV) equation, which is driven in the Itô sense by advection noise. We show that by solving certain deterministic counterparts of the modified Korteweg-de Vries with an extra diffusion term (for short DmKdV), and then combining the results with a solution of stochastic ordinary differential equations, the exact solution of the SmKdV equation may be discovered. We derive soliton solutions for the DmKdV problem using two distinct methods: the extended tanh function approach and the    exp  ⁡  (  −  ψ  (  η  )  ) -expansion method. Additionally, we study how the advection noise affects the solutions of the SmKdV equation by presenting several 3D graphs using a MATLAB program.}
}