The Dynamics of Lump, Lumpoff and Rogue Wave Solutions of (2+1)-Dimensional Hirota-Satsuma-Ito Equations

Authors

  • Ling-Di Zhang School of Mathematics, China University of Mining and Technology, Xuzhou 221116, People’s Republic of China.
  • Shou-Fu Tian School of Mathematics, China University of Mining and Technology, Xuzhou 221116, People’s Republic of China.
  • Wei-Qi Peng School of Mathematics, China University of Mining and Technology, Xuzhou 221116, People’s Republic of China.
  • Tian-Tian Zhang School of Mathematics, China University of Mining and Technology, Xuzhou 221116, P.R. China.
  • Xing-Jie Yan School of Mathematics, China University of Mining and Technology, Xuzhou 221116, People’s Republic of China.

DOI:

https://doi.org/10.4208/eajam.130219.290819

Keywords:

Lump solution, lumpoff solution, rogue wave solution, Hirota bilinear form.

Abstract

The Hirota-Satsuma-Ito equation in (2+1)-dimensions is studied and a new general representation of lump solutions is derived. If the lump soliton is generated by an exponentially localised line soliton, we obtain a lumpoff solution. On the other hand, if the lump soliton is generated by an exponentially localised twin plane soliton, we obtain a rogue solution. The appearance time and location of extreme rogue waves can be studied and predicted. Graphical examples demonstrate the dynamical behaviour of lumpoff and rogue waves.

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Published

2020-04-01

Issue

Vol. 10 No. 2 (2020)

Section

Articles