Abstract
In order to get the traveling wave solutions of the Zakharov-Kuznetsov-Benjamin-Bona-Mahony (ZK-BBM) equation, it is reduced to an ordinary differential equation (ODE) under the travelling wave transformation first. Then complete discrimination system for polynomial is applied to the ZK-BBM equation. The traveling wave solutions of the equation can be obtained.
Highlights
The nonlinear partial differential equation (PDE) is widely used to describe physical phenomena in various fields of sciences, especially in fluid mechanics, solid state physics, plasma physics, plasma waves, biology and so on
We will use complete discrimination system for polynomial proposed by Liu [1]-[4] to study the traveling wave solutions of the ZK-BBM equation
It is worth mentioning that Wazwaz [9] [10] made a detailed study for compact and noncompact physical structures and calculated the exact solutions of compact and noncompact structures by the extended tanh method for the ZK-BBM equation
Summary
The nonlinear partial differential equation (PDE) is widely used to describe physical phenomena in various fields of sciences, especially in fluid mechanics, solid state physics, plasma physics, plasma waves, biology and so on. During the past few decades, various methods have been developed by researchers to find the solutions for the NLEEs. In this article, we will use complete discrimination system for polynomial proposed by Liu [1]-[4] to study the traveling wave solutions of the ZK-BBM equation. (2014) Application of Classification of Traveling Wave Solutions to the Zakhrov-KuznetsovBenjamin-Bona-Mahony Equation. The solutions of Equation (1) have been studied in various aspects. Sadaf Bibi [7] used the Sine-cosine method to obtain the travelling wave solutions of Equation (1). It is worth mentioning that Wazwaz [9] [10] made a detailed study for compact and noncompact physical structures and calculated the exact solutions of compact and noncompact structures by the extended tanh method for the ZK-BBM equation
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