Bilinear formalism, lump solution, lumpoff and instanton/rogue wave solution of a (3+1)-dimensional B-type Kadomtsev–Petviashvili equation

TLDR: In this paper, the authors considered the simplified (3+1)-dimensional B-type Kadomtsev-Petviashvili equation and used the binary Bell polynomial theory to construct a bilinear form of the equation, and then constructed a more general lump solution that is positioned in any direction of the space to have more arbitrary autocephalous parameters.

Abstract: We consider the simplified (3+1)-dimensional B-type Kadomtsev–Petviashvili equation. We use the binary Bell polynomial theory to construct a bilinear form of the equation, and then construct a bilinear form of the special case of $$z = x$$ . In the reduced bilinear form, we constructed a more general lump solution that is positioned in any direction of the space to have more arbitrary autocephalous parameters. The lump solution can produce striped solitons, which provides a lumpoff solution. Combined with the strip solitons, we can know that when the double solitons cut the lump solution, we obtain a special rogue waves. It can be seen from our research results that the time and place of the rogue wave can be captured by tracking the moving path of the lump solution.