Dynamics of Lump Solutions, Rogue Wave Solutions and Traveling Wave Solutions for a (3 + 1)-Dimensional VC-BKP Equation
Year: 2019
Author: Ding Guo, Shou-Fu Tian, Tian-Tian Zhang
East Asian Journal on Applied Mathematics, Vol. 9 (2019), Iss. 4 : pp. 780–796
Abstract
The (3 + 1)-dimensional variable-coefficient B-type Kadomtsev-Petviashvili equation is studied by using the Hirota bilinear method and the graphical representations of the solutions. Breather, lump and rogue wave solutions are obtained and the influence of the parameter choice is analysed. Dynamical behavior of periodic solutions is visually shown in different planes. The rogue waves are determined and localised in time by a long wave limit of a breather with indefinitely large periods. In three dimensions the breathers have different dynamics in different planes. The traveling wave solutions are constructed by the Bäcklund transformation. The traveling wave method is used in construction of exact bright-dark soliton solutions represented by hyperbolic secant and tangent functions. The corresponding 3$D$ figures show various properties of the solutions. The results can be used to demonstrate the interactions of shallow water waves and the ship traffic on the surface.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.310319.040619
East Asian Journal on Applied Mathematics, Vol. 9 (2019), Iss. 4 : pp. 780–796
Published online: 2019-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Breather wave solutions rogue wave solutions lump solutions traveling wave solutions bright and dark soliton solutions.
Author Details
-
KdV Equation Model in Open Cylindrical Channel under Precession
Alshoufi, Hajar
Journal of Nonlinear Mathematical Physics, Vol. 28 (2021), Iss. 4 P.466
https://doi.org/10.1007/s44198-021-00007-8 [Citations: 2] -
Lump and rational solutions for weakly coupled generalized Kadomtsev–Petviashvili equation
Wu, Hongyu | Fei, Jinxi | Ma, WenxiuModern Physics Letters B, Vol. 35 (2021), Iss. 26 P.2150449
https://doi.org/10.1142/S0217984921504492 [Citations: 0] -
Breathers, rogue waves and their dynamics in a (2+1)-dimensional nonlinear Schrödinger equation
Chen, Yong | Wang, Xiu-Bin | Han, BoModern Physics Letters B, Vol. 34 (2020), Iss. 23 P.2050234
https://doi.org/10.1142/S0217984920502346 [Citations: 7] -
Pfaffian, soliton, hybrid and periodic-wave solutions for a ($$3+1$$)-dimensional B-type Kadomtsev–Petviashvili equation in fluid mechanics
Liu, Fei-Yan | Gao, Yi-Tian | Yu, Xin | Li, Liu-QingThe European Physical Journal Plus, Vol. 138 (2023), Iss. 1
https://doi.org/10.1140/epjp/s13360-022-03574-x [Citations: 7] -
Similarity reductions for a generalized (3+1)-dimensional variable-coefficient B-type Kadomtsev–Petviashvili equation in fluid dynamics
Gao, Xin-Yi | Guo, Yong-Jiang | Shan, Wen-RuiChinese Journal of Physics, Vol. 77 (2022), Iss. P.2707
https://doi.org/10.1016/j.cjph.2022.04.014 [Citations: 34] -
Bilinear auto-Bäcklund transformations and the hybrid localized wave solutions for the ($$3+1$$)-dimensional B-type Kadomtsev–Petviashvili equation
Ma, Hongcai | Su, Nan | Deng, AipingOptical and Quantum Electronics, Vol. 55 (2023), Iss. 12
https://doi.org/10.1007/s11082-023-05440-1 [Citations: 2] -
Bäcklund transformations, kink soliton, breather- and travelling-wave solutions for a (3+1)-dimensional B-type Kadomtsev–Petviashvili equation in fluid dynamics
Ma, Yong-Xin | Tian, Bo | Qu, Qi-Xing | Wei, Cheng-Cheng | Zhao, XinChinese Journal of Physics, Vol. 73 (2021), Iss. P.600
https://doi.org/10.1016/j.cjph.2021.07.001 [Citations: 51]