The coupled Boussinesq equation and its Darboux transformation on the time–space scale - Huang, Xiaoqian; Zhang, Yong; Dong, Huanhe (Frontiers in Physics, 2022)
Gel’fand-Dikii (GD) formalism is an approach for generating integrable systems in terms of fractional powers of δ differential operator. In this paper, it is extending the GD formalism associated with third-order δ differential operator L to time scale. Then the coupled Boussinesq equation on time-space scale is given by taking special values, and it can be reduced on different space-time scales. What’s more, the exact solutions of coupled Boussinesq equation on timespace scale and the classical Boussinesq equation are constructed via employing the extensions of Darboux theorem and Crum theorem on time scale