TITLE:
Abundant Lump Solutions and Interaction Phenomena to the Kadomtsev-Petviashvili-Benjamin-Bona-Mahony Equation
AUTHORS:
Jianqing Lü, Sudao Bilige, Xiaoqing Gao, Yuexing Bai, Runfa Zhang
KEYWORDS:
Lump Solution, KP-BBM Equation, Hirota Bilinear Form, Interaction Phenomenon, Breather Soliton
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.6 No.8,
August
29,
2018
ABSTRACT:
In this paper, we obtained a kind of lump solutions of the
Kadomtsev-Petviashvili-Benjamin-Bona-Mahony
(KP-BBM) equation with the assistance of Mathematica. Some contour plots with
different determinant values are sequentially made to show that the
corresponding lump solutions tend to zero when x2+y2→∞. Particularly, lump solutions
with specific values of the include parameters are plotted, as illustrative
examples. Finally, a combination of stripe soliton and lump soliton is
discussed to the KP-BBM equation, in which such a solution presents two different
interesting phenomena: lump-kink and lump-soliton. Simultaneously, breather
rational soliton solutions are displayed.