Dynamic Behaviors of the Dark Higher Order Rogue Waves and Interaction Inductions of a (3 + 1)‐Dimensional Model

ABSTRACT The research obtained dark second‐order rogue waves and two sets of interaction solutions for (3 + 1)‐dimensional equation by using symbolic calculation and two induction formulas. The two sets of interaction solutions are about second‐order rogue waves and multiple stripes, second‐order rogue waves and multiple solitons. Six sets of composite diagrams are made to show the interactions in three dimensions. The second‐order rogue waves merge from two low‐amplitude tops into one high‐amplitude top if they meet with multiple stripes, and the amplitude increases with the increase of stripes' number. The second‐order rogue waves are usually generated in the center of two kinky solitons if they meet with multiple solitons, and the amplitude increases with the increase of solitons' number. No matter what kind of rendezvous, we see the energy transfer from solitons to rogue waves and back to solitons. This will be useful in studying the evolution of rogue wave.