Rational Wave Solutions and Dynamics Properties of the Generalized ( 2 + 1 )-Dimensional Calogero-Bogoyavlenskii-Schiff Equation by Using Bilinear Method

Lihui Han,Sudao Bilige,Runfa Zhang,Meiyu Li,Xiaomin Wang

doi:10.1155/2021/9295547

Abstract

Through symbolic computation with Maple, fifty-seven sets of rational wave solutions to the generalized Calogero-Bogoyavlenskii-Schiff equation are presented by employing the generalized bilinear operator when the parameter p = 2 . Via the three-dimensional plots and contour plots with the help of Maple, the dynamics of these solutions are described very well. These solutions have greatly enriched the exact solutions of the generalized Calogero-Bogoyavlenskii-Schiff equation on the existing literature. The result will be widely used to describe many nonlinear scientific phenomena.

Highlights

It is well known that nonlinear evolution equations (NLEEs) play an important and significant role in describing nonlinear scientific phenomena, such as fluid dynamics, plasma physics, chemistry, marine engineering, optics, and physics
By using a transformation of the potential function of NLEEs and the definition and properties of the D operator, NLEEs are written in bilinear form, and the single-double-multiple soliton solutions of NLEEs can be obtained by using the small parameter expansion method
The 3D plots and contour plots in Figures 1 and 2 are given to display the dynamic process of the rogue wave, and the rational wave solutions contribute to the study of multidimensional and higher-order rogue waves

Summary

Introduction

It is well known that nonlinear evolution equations (NLEEs) play an important and significant role in describing nonlinear scientific phenomena, such as fluid dynamics, plasma physics, chemistry, marine engineering, optics, and physics. By using a transformation of the potential function of NLEEs and the definition and properties of the D operator, NLEEs are written in bilinear form, and the single-double-multiple soliton solutions of NLEEs can be obtained by using the small parameter expansion method.

Bilinear Form of the gCBS Equation

Rational Wave Solutions for the gCBS Equation

Conclusion and Outlook