From the point of view of two distinct methods, we will construct new multiple types of private exact solutions of the (2+1)-dimensional modified Zakharov–Kuznetsov equation (MZKE) which is a famous model in plasma physics. The suggested methods for this purpose are the extended simple equation method (ESEM) and the Paul–Painleve approach method (PPAM). Moreover, the numerical solutions corresponding to the achieved solutions are demonstrated in the framework of the variational iteration method (VIM). Furthermore, we will demonstrate a good comparison not only between our achieved solutions but also with that realized previously by other authors who studied this model before.

中文翻译：

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(2+1)维修正的Zakharov-Kuznetsov方程的多种精确解

从两种截然不同的方法的角度，我们将构造等离子体物理学著名模型（2+1）维修正的扎哈罗夫-库兹涅佐夫方程（MZKE）的新的多种私有精确解。为此目的建议的方法是扩展简单方程法 (ESEM) 和 Paul-Painleve 方法 (PPAM)。此外，在变分迭代法（VIM）的框架下，证明了与所获得的解相对应的数值解。此外，我们不仅将展示我们实现的解决方案之间的良好比较，而且还将展示与之前研究过该模型的其他作者之前实现的解决方案之间的良好比较。