Diversity of Interaction Solutions of a Shallow Water Wave Equation
Jian-Ping Yu,
Wen-Xiu Ma,
Bo Ren,
Yong-Li Sun,
Chaudry Masood Khalique
Affiliations
Jian-Ping Yu
Department of Applied Mathematics, University of Science and Technology Beijing, Beijing 100083, China
Wen-Xiu Ma
Department of Mathematics, Zhejiang Normal University, Jinhua 321004, Zhejiang, China
Bo Ren
Institute of Nonlinear Science, Shaoxing University, Shaoxing 312000, China
Yong-Li Sun
Department of Mathematics, Beijing University of Chemical Technology, Beijing 100029, China
Chaudry Masood Khalique
International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X2046, Mmabatho 2735, South Africa
In this paper, we study the diversity of interaction solutions of a shallow water wave equation, the generalized Hirota–Satsuma–Ito (gHSI) equation. Using the Hirota direct method, we establish a general theory for the diversity of interaction solutions, which can be applied to generate many important solutions, such as lumps and lump-soliton solutions. This is an interesting feature of this research. In addition, we prove this new model is integrable in Painlevé sense. Finally, the diversity of interactive wave solutions of the gHSI is graphically displayed by selecting specific parameters. All the obtained results can be applied to the research of fluid dynamics.
