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Volume 10, Issue 2
The Dynamics of Lump, Lumpoff and Rogue Wave Solutions of (2+1)-Dimensional Hirota-Satsuma-Ito Equations

Ling-Di Zhang, Shou-Fu Tian, Wei-Qi Peng, Tian-Tian Zhang & Xing-Jie Yan

DOI: 10.4208/eajam.130219.290819

East Asian J. Appl. Math., 10 (2020), pp. 243-255.

Published online: 2020-04

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  • 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.

  • Keywords

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

  • AMS Subject Headings

35Q51, 35Q53, 35C99, 68W30, 74J35

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

ldzhang@cumt.edu.cn (Ling-Di Zhang)

sftian@cumt.edu.cn., shoufu2006@126.com (Shou-Fu Tian)

ts17080018a3@cumt.edu.cn (Wei-Qi Peng)

ttzhang@cumt.edu.cn (Tian-Tian Zhang)

yanxj04@cumt.edu.cn (Xing-Jie Yan)

  • BibTex
  • RIS
  • TXT
@Article{EAJAM-10-243, author = {Zhang , Ling-DiTian , Shou-FuPeng , Wei-QiZhang , Tian-Tian and Yan , Xing-Jie}, title = {The Dynamics of Lump, Lumpoff and Rogue Wave Solutions of (2+1)-Dimensional Hirota-Satsuma-Ito Equations}, journal = {East Asian Journal on Applied Mathematics}, year = {2020}, volume = {10}, number = {2}, pages = {243--255}, 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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.130219.290819}, url = {http://global-sci.org/intro/article_detail/eajam/16136.html} }
TY - JOUR T1 - The Dynamics of Lump, Lumpoff and Rogue Wave Solutions of (2+1)-Dimensional Hirota-Satsuma-Ito Equations AU - Zhang , Ling-Di AU - Tian , Shou-Fu AU - Peng , Wei-Qi AU - Zhang , Tian-Tian AU - Yan , Xing-Jie JO - East Asian Journal on Applied Mathematics VL - 2 SP - 243 EP - 255 PY - 2020 DA - 2020/04 SN - 10 DO - http://doi.org/10.4208/eajam.130219.290819 UR - https://global-sci.org/intro/article_detail/eajam/16136.html KW - Lump solution, lumpoff solution, rogue wave solution, Hirota bilinear form. AB -

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.

Zhang , Ling-DiTian , Shou-FuPeng , Wei-QiZhang , Tian-Tian and Yan , Xing-Jie. (2020). The Dynamics of Lump, Lumpoff and Rogue Wave Solutions of (2+1)-Dimensional Hirota-Satsuma-Ito Equations. East Asian Journal on Applied Mathematics. 10 (2). 243-255. doi:10.4208/eajam.130219.290819
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