Rogue Waves and Lump Solitons of the (3+1)-Dimensional Generalized B-type Kadomtsev-Petviashvili Equation for Water Waves

摘要

In this paper,the (3 + 1)-dimensional generalized B-type Kadomtsev-Petviashvili equation for water waves is investigated.Through the Hirota method and Kadomtsev-Petviashvili hierarchy reduction,we obtain the first-order,higher-order,multiple rogue waves and lump solitons based on the solutions in terms of the Gramian.The first-order rogue waves are the line rogue waves which arise from the constant background and then disappear into the constant background again,while the first-order lump solitons propagate stably.Interactions among several first-order rogue waves which are described by the multiple rogue waves are presented.Elastic interactions of several first-order lump solitons are also presented.We find that the higher-order rogue waves and lump solitons can be treated as the superpositions of several first-order ones,while the interaction between the second-order lump solitons is inelastic.