Some novel exact solutions for the generalized time-space fractional coupled Hirota-Satsuma KdV equation - Cheng, Yueling; Hong, Siyuan; Yang, Shujun; Chi, Xu; Yang, Jinghao (Frontiers in Physics, 2025)
In this paper, two efficient methods, namely the modified G′/G,1/G-expansion method and the G′/bG′+G+a-expansion method, are employed to obtain novel exact wave solutions for the generalized time-space fractional coupled Hirota-Satsuma KdV equation. Various types of analytical explicit solutions, including well-known bell-shape solitons, mixed solitary wave solutions, and periodic wave solutions are obtained. These solutions are of great significance for revealing the nonlinear interaction between two long waves with different dispersion effects. The two-dimensional and three-dimensional distribution maps and contour plots corresponding to partial solutions are simulated to visually display the evolution process of relevant physical quantities over time. Moreover, the potential applications of these solutions in nano/micro devices and systems, especially in MEMS (Micro-Electro-Mechanical Systems) are discussed. It is demonstrated that the methods and processes utilized have strong applicability for constructing analytical solutions of nonlinear evolution equations.