Residual symmetry, interaction solutions, and conservation laws of the (2+1)-dimensional dispersive long-wave system

We explore the (2+1)-dimensional dispersive long-wave (DLW) system. From the standard truncated Painlevé expansion, the Bäcklund transformation (BT) and residual symmetries of this system are derived. The introduction to an appropriate auxiliary dependent variable successfully localizes the residual symmetries to Lie point symmetries. In particular, it is verified that the (2+1)-dimensional DLW system is consistent Riccati expansion (CRE) solvable. If the special form of (CRE)-consistent tanh-function expansion (CTE) is taken, the soliton-cnoidal wave solutions and corresponding images can be explicitly given. Furthermore, the conservation laws of the DLW system are investigated with symmetries and Ibragimov theorem.