In this article, we execute the enhanced ($G\text{'}/G$)-expansion method to search for new and further general closed-form wave solutions to the nonlinear partial differential equation, namely the Benny Luke equation. This method is one of the powerful techniques that come into view in recent time for establishing more exact wave solutions to nonlinear partial differential equations. We have achieved some new exact solutions including soliton and periodic wave solutions with arbitrary parameters and the solutions are expressed in terms of hyperbolic and trigonometric functions. The efficiency of this method for finding exact solutions has been established. It is shown that the enhanced ($G\text{'}/G$)-expansion method is direct, effective and can be used for many other nonlinear partial differential equations in mathematical physics and engineering.

在本文中，我们执行增强的 ($G\text{'}/G$)-展开方法来寻找非线性偏微分方程的新的和更进一步的一般封闭形式的波解，即 Benny Luke 方程。这种方法是最近出现的一种强大的技术，用于建立非线性偏微分方程的更精确的波解。我们已经实现了一些新的精确解，包括具有任意参数的孤子解和周期波解，并且这些解用双曲函数和三角函数表示。已经建立了该方法寻找精确解的效率。结果表明，增强的 ($G\text{'}/G$)-展开法直接、有效，可用于数学物理和工程中的许多其他非线性偏微分方程。