Rogue waves of a (3+1)-dimensional BKP equation |
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| Affiliation: | 1.Department of Mathematics, China University of Mining and Technology(Beijing), Beijing 100083, China;2.School of Science, Beijing Forestry University, Beijing 100083, China;3.Department of Mathematics and Physics, North China Electric Power University, Baoding 071003, China |
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| Abstract: | We investigate certain rogue waves of a (3+1)-dimensional BKP equation via the Kadomtsev-Petviashili hierarchy reduction method. We obtain semi-rational solutions in the determinant form, which contain two special interactions: (i) one lump develops from a kink soliton and then fuses into the other kink one; (ii) a line rogue wave arises from the segment between two kink solitons and then disappears quickly. We find that such a lump or line rogue wave only survives in a short time and localizes in both space and time, which performs like a rogue wave. Furthermore, the higher-order semi-rational solutions describing the interaction between two lumps (one line rogue wave) and three kink solitons are presented. |
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| Keywords: | (3+1)-dimensional BKP equation Kadomtsev-Petviashvili hierarchy reduction interaction rogue wave lump |
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