**Jianxi YuThis email address is being protected from spambots. You need JavaScript enabled to view it.**

Institute of Engineering and Economics, Henan Institute of Economics and Trade, Zhengzhou, Henan, 450018, China

Received:
June 28, 2022

Accepted:
August 5, 2022

Publication Date:
October 14, 2022

* ***Copyright **The Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited.

Download Citation: ||https://doi.org/10.6180/jase.202307_26(7).0009

**ABSTRACT**

The generalized algebra technique is used to search for exact wave solutions of the ZK-BBM equation in this article. This equation is a notable model for describing the acoustic waves in harmonic crystals, shallow water waves etc. By applying the wave transformation, we obtained an ordinary differential equation. We have successfully obtained many exact wave solutions with arbitrary parameters by the method that exact wave solutions are expressed in terms of generalized hyperbolic function solution, generalized trigonometric function solution, exponential function solution, and rational function solution. The results show that the generalized algebra technique is a very concise and powerful mathematical tool for nonlinear evolution equations in engineering and science.

Keywords:
ZK-BBM equation; generalized algebra technique; exact wave solution

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