Abstract
In this paper, we consider a family of rational solution for an extend (3 + 1)-dimensional B-type Kadomtsev-Petviashvili-Boussinesq equation with two non-zero offset parameters μ and ν, through its bilinear form and symbolic computation. These solutions can be classified as multi-order breather and multi-order rogue wave. The existence of μ, ν brings nontrivial change to the shape of the higher order solution. The higher order ones are able to decompose into several well-separated breathers and each of them symmetrically locates on a circle. In addition, we analyze their scatter behavior, the moving path of the extreme values as well as the inner connection between the bilinear equation and the rogue wave.
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