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

Abstract

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-Bäcklund transformation. Via the truncated Painlevé expansion, we get a Painlevé-type auto-Bäcklund 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.