https://doi.org/10.1140/epjp/s13360-020-00300-3
Regular Article
Twisted lump, lumpoff and rogue wave of the (2+1)-dimensional Kaup–Kupershmidt equation
1
Department of Mathematics and Institute of Nonlinear Analysis, Lishui University, Lishui, 323000, China
2
Department of Physics, Zhejiang Normal University, Jinhua, 321004, China
3
Ningbo Collaborative Innovation Center of Nonlinear Hazard System of Ocean and Atmosphere, Ningbo University, Ningbo, 315211, China
* e-mail: linji@zjnu.edu.cn
Received:
16
September
2019
Accepted:
26
February
2020
Published online:
6
March
2020
Exact explicit rational and resonant rational–exponential solutions of the (2+1)-dimensional Kaup–Kupershmidt equation are derived by using the bilinear method. In addition to single-peak and double-peak lumps, the fundamental rational solution is shown to depict a twisted lump structure including two interactional single-peak lumps. The first resonant solution is able to describe a twisted lumpoff in which the twisted lump is cut by one line soliton and the moving path and velocities of lump, as well as the approximate starting time of interaction can be calculated. The second resonant solution allows a special interaction that the twisted lump is cut by two line solitons in opposite directions. This fascinating interaction is identified as a twisted rogue wave with the predictability, because the emerging time, location and moving route of lump can be caught exactly. Moreover, the condition of the existence of rogue wave indicates that it contains regular and reduced cases.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2020
