Diversity of Interaction Solutions of a Shallow Water Wave Equation

Author:

Yu Jian-Ping1,Ma Wen-Xiu23456ORCID,Ren Bo7ORCID,Sun Yong-Li89ORCID,Khalique Chaudry Masood6ORCID

Affiliation:

1. Department of Applied Mathematics, University of Science and Technology Beijing, Beijing 100083, China

2. Department of Mathematics, Zhejiang Normal University, Jinhua 321004, Zhejiang, China

3. Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620, USA

4. School of Mathematics, South China University of Technology, Guangzhou 510640, China

5. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, Shandong, China

6. International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X2046, Mmabatho 2735, South Africa

7. Institute of Nonlinear Science, Shaoxing University, Shaoxing 312000, China

8. Department of Mathematics, Beijing University of Chemical Technology, Beijing 100029, China

9. Department of Mathematics and Statistics, Brock University, Saint Catharines, ON, Canada

Abstract

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.

Funder

National Natural Science Foundation of China

Publisher

Hindawi Limited

Subject

Multidisciplinary,General Computer Science

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