Bäcklund Transformations, Nonlocal Symmetries and Soliton–Cnoidal Interaction Solutions of the (2 + 1)-Dimensional Boussinesq Equation

Under investigation in this paper are the nonlocal symmetries and consistent Riccati expansion integrability of the (2 + 1)-dimensional Boussinesq equation, which can be used to describe the propagation of long waves in shallow water. By constructing the Bäcklund transformation, we obtain the truncated Painlevé expansion of the system. Its Schwarzian form is also derived, whose nonlocal symmetry is localized to provide the corresponding nonlocal group. Furthermore, we verify that the system is solvable via the consistent Riccati expansion (CRE). Based on the CRE, the interaction solutions between soliton and cnoidal periodic wave are explicitly studied.