New Exact Solutions of the Drinfeld-Sokolov System by the Generalized Unified Method

Abstract

In this study, we apply the generalized unified method (GUM), an enhanced version of the unified method, to find novel exact solutions of the Drinfeld-Sokolov System (DSS) that models the dispersive water waves in fluid dynamics. Moreover, 3D and 2D graphs of some of the obtained exact solutions are plotted to present how various characteristic forms they have. The results show that the presented method simplifies the computation process on the computer in a highly reliable and straightforward manner while providing the solutions in more general forms. In addition, the GUM has great potential to apply to a wide range of problems, including nonlinear partial differential equations (NPDEs) and fractional partial differential equations (FPDEs) for finding exact solutions.