Lump, mixed lump-stripe, mixed rogue wave-stripe and breather wave solutions for a (3+1)-dimensional generalized Calogero–Bogoyavlenskii–Schiff equation

Abstract

In this paper, the investigation is made on a (3[Formula: see text]+[Formula: see text]1)-dimensional generalized Calogero–Bogoyavlenskii–Schiff equation. We obtain the lump, mixed lump-stripe, mixed rogue wave-stripe and breather wave solutions via the Hirota method and symbolic computation. Accordingly, we observe that the shape and amplitude of the lump keep unchanged, while the mixed lump-stripe solutions present that (1) the lump/stripe and one-stripe waves fuse into a one-stripe wave; (2) the one-stripe wave splits into a lump/stripe and a one-stripe wave. We graphically show the interaction between a rogue wave and a pair of stripe waves, and observe that the amplitude of the rogue wave reaches the maximum value at a certain position. Besides, the breather wave propagates steadily in a certain direction.