Mixed lump-kink and rogue wave-kink solutions for a (3 + 1) -dimensional B-type Kadomtsev-Petviashvili equation in fluid mechanics
State Key Laboratory of Information Photonics and Optical Communications, and School of Science, Beijing University of Posts and Telecommunications, 100876, Beijing, China
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Accepted: 12 January 2018
Published online: 6 February 2018
Under investigation is a (3 + 1) -dimensional B-type Kadomtsev-Petviashvili equation, which describes the weakly dispersive waves in a fluid. Via the Hirota method and symbolic computation, we obtain the mixed lump-kink and mixed rogue wave-kink solutions. Through the mixed lump-kink solutions, we observe three different phenomena between a lump and one kink. For the fusion phenomenon, a lump and a kink are merged with the lump’s energy transferring into the kink gradually, until the lump merges into the kink completely. Fission phenomenon displays that a lump separates from a kink. The last phenomenon shows that a lump travels together with a kink with their amplitudes unchanged. In addition, we graphically study the interaction between a rogue wave and a pair of the kinks. It can be observed that the rogue wave arises from one kink and disappears into the other kink. At certain time, the amplitude of the rogue wave reaches the maximum.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2018