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Volume 9, Issue 4
Dynamics of Lump Solutions, Rogue Wave Solutions and Traveling Wave Solutions for a (3 + 1)-Dimensional VC-BKP Equation

Ding Guo, Shou-Fu Tian & Tian-Tian Zhang

East Asian J. Appl. Math., 9 (2019), pp. 780-796.

Published online: 2019-10

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  • 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.

  • AMS Subject Headings

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

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

TS17080009A3@cumt.edu.cn (Ding Guo)

sftian@cumt.edu.cn (Shou-Fu Tian)

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

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@Article{EAJAM-9-780, author = {Guo , DingTian , Shou-Fu and Zhang , Tian-Tian}, title = {Dynamics of Lump Solutions, Rogue Wave Solutions and Traveling Wave Solutions for a (3 + 1)-Dimensional VC-BKP Equation}, journal = {East Asian Journal on Applied Mathematics}, year = {2019}, volume = {9}, number = {4}, pages = {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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.310319.040619}, url = {http://global-sci.org/intro/article_detail/eajam/13332.html} }
TY - JOUR T1 - Dynamics of Lump Solutions, Rogue Wave Solutions and Traveling Wave Solutions for a (3 + 1)-Dimensional VC-BKP Equation AU - Guo , Ding AU - Tian , Shou-Fu AU - Zhang , Tian-Tian JO - East Asian Journal on Applied Mathematics VL - 4 SP - 780 EP - 796 PY - 2019 DA - 2019/10 SN - 9 DO - http://doi.org/10.4208/eajam.310319.040619 UR - https://global-sci.org/intro/article_detail/eajam/13332.html KW - Breather wave solutions, rogue wave solutions, lump solutions, traveling wave solutions, bright and dark soliton solutions. AB -

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.

DingGuo, Shou-FuTian & Tian-TianZhang. (2019). Dynamics of Lump Solutions, Rogue Wave Solutions and Traveling Wave Solutions for a (3 + 1)-Dimensional VC-BKP Equation. East Asian Journal on Applied Mathematics. 9 (4). 780-796. doi:10.4208/eajam.310319.040619
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