University of Tabriz Computational Methods for Differential Equations 2345-3982 13 1 2024 11 01 Soliton solutions to the DS and generalized DS system via an analytical method 233 248 17834 10.22034/cmde.2024.60337.2576 EN Ilyos Sultanovich Abdullayev Department of Management and Marketing, Faculty of Social and Economic Sciences, Urgench State University, Urgench, 220100, Uzbekistan. Elvir Munirovich Akhmetshin Department of Economics and Management, Faculty of Economic and Legal Sciences Kazan Federal University, Elabuga Institute of KFU, 423604, Elabuga, Russian Federation, Republic of Tatarstan. Evgeny Efimovich Krasnovskiy Department of Applied Mathematics, Bauman Moscow State Technical University, Russian Federation. Nalbiy Salikhovich Tuguz Department of Higher Mathematics, Kuban State Agrarian University named after I.T. Trubilin, Krasnodar region, 350044, Russian Federation. Galina Mashentseva Department of Economics and Humanities, Faculty of Higher Education Kamyshin Technological Institute (branch of) Volgograd State Technical University, Russian Federation. Journal Article 2024 01 30 In this article, the exact solutions for nonlinear Drinfeld-Sokolov (DS) and generalized Drinfeld-Sokolov (gDS) equations are established. The rational Exp-function method (EFM) is used to construct solitary and soliton solutions of nonlinear evolution equations. This method is developed for searching exact traveling wave solutions of nonlinear partial differential equations. Also, exact solutions with solitons and periodic structures are obtained. The obtained results are not only presented numerically but are also accompanied by insightful physical interpretations, enhancing the understanding of the complex dynamics described by these mathematical models. The utilization of the rational EFM and the broad spectrum of obtained solutions contribute to the depth and significance of this research in the field of nonlinear wave equations. https://cmde.tabrizu.ac.ir/article_17834_5a01fcc5e21ce1ba7ca27896fac84ad4.pdf