Backlund transformations, kink soliton, breather- and travelling-wave solutions for a (3+1)-dimensional B-type Kadomtsev-Petviashvili equation in fluid dynamics

In this paper, we investigate a (3+1)-dimensional B-type Kadomtsev-Petviashvili (BKP) equation in fluid dynamics. Based on the Hirota method, we give a bilinear auto-Backlund transformation. Via the truncated Painleve expansion, we get a Painleve-type auto-Backlund transformation. With the aid of the symbolic computation, we derive some one-and two-kink soliton solutions. We present the oblique and parallel elastic interactions between the two-kink solitons. Via the extended homoclinic test technique, we construct some breather-wave solutions. Besides, we derive some lump solutions with the periods of the breather-wave solutions to the infinity. We observe that the shapes of a breather wave and a lump remain unchanged during the propagation. Based on the polynomial-expansion method, travelling-wave solutions are constructed.