4.3 Article

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
Volume 9, Issue 4, Pages 780-796

Publisher

GLOBAL SCIENCE PRESS
DOI: 10.4208/eajam.310319.040619

Keywords

Breather wave solutions; rogue wave solutions; lump solutions; traveling wave solutions; bright and dark soliton solutions

Funding

  1. Postgraduate Research and Practice of Educational Reform for Graduate Students in CUMT [2019YJSJG046]
  2. Natural Science Foundation of Jiangsu Province [BK20181351]
  3. Six Talent Peaks Project in Jiangsu Province [JY-059]
  4. Qinglan Project of Jiangsu Province of China
  5. National Natural Science Foundation of China [11975306]
  6. Fundamental Research Fund for the Central Universities [2019ZDPY07, 2019QNA35]
  7. China Postdoctoral Science Foundation [2015M570498, 2017T100413]

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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 Backlund transformation. The traveling wave method is used in construction of exact bright-dark soliton solutions represented by hyperbolic secant and tangent functions. The corresponding 3D 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.

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