Symmetry Groups and Exact Solutions of New (4+1)-Dimensional Fokas Equation

In this paper, we investigate symmetries of the new (4+1)-dimensional Fokas equation, including point symmetries and the potential symmetries. We firstly employ the algorithmic procedure of computing the point symmetries. And then we transform the Fokas equation into a potential system and gain the potential symmetries of Fokas equation. Finally, we use the obtained point symmetries and some constructive methods to get some doubly periodic wave solutions and other solutions of the Fokas equation. In particular, some solitary wave solutions are also given. (general)