Localized excitation and folded solitary wave for an extended (3+1)-dimensional B-type Kadomtsev–Petviashvili equation

In this work, we employ the multi-linear variable separation approach to derive variable separation solution for a new extended (3+1)-dimensional B-type Kadomtsev–Petviashvili equation. The solutions obtained here contain two totally separated arbitrary functions without any constraint. In addition, three kinds of localized excitations have been constructed, including dromion-lattice structure, lump-lattice structure and periodic lattice structure. By adjusting the velocities to be equal or unequal, the chase-collision and interaction phenomena have been observed. Moreover, folded solitary waves such as worm shape, worm-dromion shape, worm-solitoff shape, fin shape and octopus shape foldons are derived by introducing multi-valued function. Lastly, we discuss the interaction behavior of two- and three-foldon and construct M× N folded wave.