In this paper, a new solution process of $(1/G^{\prime })$ -expansion and $(G^{\prime }/G,1/G)$ -expansion methods has been proposed for the analytic solution of the Zhiber-Shabat (Z-S) equation. Rather than the classical $(G^{\prime }/G,1/G)$ -expansion method, a solution function in different formats has been produced with the help of the proposed process. New complex rational, hyperbolic, rational and trigonometric types solutions of the Z-S equation have been constructed. By giving arbitrary values to the constants in the obtained solutions, it can help to add physical meaning to the traveling wave solutions, whereas traveling wave has an important place in applied sciences and illuminates many physical phenomena. 3D, 2D and contour graphs are displayed to show the stationary wave or the state of the wave at any moment with the values given to these constants. Conditions that guarantee the existence of traveling wave solutions are given. Comparison of $(G^{\prime }/G,1/G)$ -expansion method and $(1/G^{\prime })$ -expansion method, which are important instruments in the analytical solution, has been made. In addition, the advantages and disadvantages of these two methods have been discussed. These methods are reliable and efficient methods to obtain analytic solutions of nonlinear evolution equations (NLEEs).

中文翻译：

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Zhiber-Shabat方程的不同类型解析解的构造

本文提出了一种新的解决方案 $（\mathrm{1个}/G^{\prime }）$ -扩展和 $（G^{\prime }/G，\mathrm{1个}/G）$ 对于Zhiber-Shabat（ZS）方程的解析解，已经提出了扩展方法。而不是古典 $（G^{\prime }/G，\mathrm{1个}/G）$ -扩展方法，借助于所提出的过程已经产生了不同格式的求解函数。构造了ZS方程的新的复有理，双曲，有理和三角型解。通过给获得的解中的常数赋予任意值，可以帮助在行波解中增加物理意义，而行波在应用科学中占有重要地位，并阐明了许多物理现象。显示3D，2D和轮廓图，以随时显示固定波或波的状态，并赋予这些常数值。给出了保证行波解存在的条件。相对比 $（G^{\prime }/G，\mathrm{1个}/G）$ 扩展方法和 $（\mathrm{1个}/G^{\prime }）$ 扩展方法已经成为分析解决方案中的重要工具。此外，还讨论了这两种方法的优缺点。这些方法是获得非线性发展方程（NLEE）解析解的可靠而有效的方法。