Diversity of Interaction Solutions of a Shallow Water Wave Equation

Jian-Ping Yu,Wen-Xiu Ma,Bo Ren,Yong-Li Sun,Chaudry Masood Khalique

doi:10.1155/2019/5874904

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.

Highlights

Introduction eHirota method played an important role in solving partial di erential equations [1]
We found that the lump wave is analytic in the XY-plane if and only if c1 ≠ 0 and b1 ≠ 0. e aforementioned lump-soliton solution is an interactive solution; during the collision, they interact like fusion and fission phenomenon in physics
We introduced a shallow water wave equation, the generalized Hirota–Satsuma–Ito (gHSI) equation (3), and established the theory of its diversity of interactions, the lump solution, and lumpsoliton solutions

Summary

Introduction

Introduction eHirota method played an important role in solving partial di erential equations [1]. We will establish the general theory of interaction solutions of equation (3) so that we can build a general method to find the interaction solutions between lumps and other types of solutions of the (2 + 1)-dimensional gHSI equation by using the Hirota direct approach. The diversity of the interaction solutions of the gHSI equation is illustrated vividly by some graphs.

Results

Conclusion