Infinite generation of soliton-like solutions for the (2+1) -dimensional generalized Broer–Kaup system

There is a long-standing interest in obtaining exact analytical solutions of nonlinear evolution equations since the exact solutions often model natural phenomena and facilitate the testing of numerical solvers as well as aiding in the stability analysis. In this paper, using a Burgers equation-based constructive method, we obtain a formula which can be applied to generate infinite sequences of exact solutions for the (2+1)-dimensional generalized Broer–Kaup (GBK) system. According to some explicit exact solutions, we also graphically reveal some interesting soliton-like wave motions which may be observable in the future experiments.