Symmetry analysis and CTE solvability for the (2+1)-dimensional Boiti–Leon–Pempinelli equation

The residual symmetry is derived from the known truncated Painlevé expansion of the (2+1)-dimensional Boiti–Leon–Pempinelli (BLP) equation, and this kind of residual symmetry is localized by introducing two new variables. By applying the Lie point symmetry method to the enlarged system, a new type of finite symmetry transformation is derived. Moreover, it is proved that the (2+1)-dimensional BLP equation is consistent tanh expansion solvable, the exact interaction solutions between solitons and any other types of potential Burgers waves are also obtained, which include soliton-error function waves, soliton-periodic waves, and so on.