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Rogue Waves in the Three-Dimensional Kadomtsev–Petviashvili Equation |
| Chao Qian, Ji-Guang Rao, Yao-Bin Liu, Jing-Song He** |
Department of Mathematics, Ningbo University, Ningbo 315211
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Chao Qian, Ji-Guang Rao, Yao-Bin Liu et al 2016 Chin. Phys. Lett. 33 110201 |
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Abstract Breathers and rogue waves as exact solutions of the three-dimensional Kadomtsev–Petviashvili equation are obtained via the bilinear transformation method. The breathers in three dimensions possess different dynamics in different planes, such as growing and decaying periodic line waves in the $(x,y)$, $(x,z)$ and $(y,t)$ planes. Rogue waves are localized in time, and are obtained theoretically as a long wave limit of breathers with indefinitely larger periods. It is shown that the rogue waves possess growing and decaying line profiles in the $(x,y)$ or $(x,z)$ plane, which arise from a constant background and then retreat back to the same background again.
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Received: 30 July 2016
Published: 28 November 2016
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| Fund: Supported by the National Natural Science Foundation of China under Grant No 11271210, and the K. C. Wong Magna Fund in Ningbo University. |
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