TY - JOUR TI - A variable coefficient mKdV dynamic model for non-linear long wave AU - Wu Shu-Hao AU - Zhao Bao-Jun JN - Thermal Science PY - 2024 VL - 28 IS - 4 SP - 3411 EP - 3415 PT - Article AB - In this paper, we obtained a variable coefficient partial differential model that characterizes non-linear long waves with topography effects through the multi-scale perturbation expansion method, especially the new model caused by the variation of background shear flow over time. Next, the expansion Jacobian elliptic function method is used to provide an analytical solution for the model and analyze its wave characteristics.