Painlevé Property, Bäcklund Transformations and Rouge Wave Solutions of (3 + 1)-Dimensional Burgers Equation

Burgers equation is the simplest one in soliton theory, which has been widely applied in almost all the physical branches. In this paper, we discuss the Painlevé property of the (3+1)-dimensional Burgers equation, and then Bäcklund transformation is derived according to the truncated expansion of the obtained Painlevé analysis. Using the Bäcklund transformation, we find the rouge wave solutions to the equation via the multilinear variable separation approach. And we also give an exact solution obtained by general variable separation approach, which is proved to possess abundant structures. (general)