In this article, the unified method, the improved F-expansion method and the modified Kudryashov method are used to obtain the traveling wave solutions of the generalized Zakharov–Kuznetsov equation with variable coefficients. Different types of traveling wave solutions are derived including polynomial solutions and rational solutions by applying the unified method. The polynomial solutions include solitary wave solutions, soliton wave solutions and elliptic wave solutions, and the rational solutions contain periodic type rational solutions and soliton type rational solutions. By means of the improved F-expansion method with Riccati equation, the hyperbolic trigonometric solutions, trigonometric solutions and rational solutions are obtained containing several free parameters. The modified Kudryashov method is also applied to obtain new traveling wave solutions. In addition, the properties of several solutions are represented graphically with the appropriate parameters.

中文翻译：

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具有可变系数的 $$(2+1)$$ 维广义 Zakharov-Kuznetsov 方程的行波解

本文采用统一法、改进的F-展开法和改进的Kudryashov 法得到广义变系数Zakharov-Kuznetsov方程的行波解。应用统一方法推导出不同类型的行波解，包括多项式解和有理解。多项式解包括孤波解、孤子波解和椭圆波解，有理解包括周期型有理解和孤子型有理解。利用Riccati方程改进F展开法，得到了包含多个自由参数的双曲三角解、三角解和有理解。改进的 Kudryashov 方法也用于获得新的行波解。此外，几个解决方案的属性用适当的参数以图形方式表示。