In this paper, the Kudryashov method to construct the new exact solitary wave solutions for the newly developed ()-dimensional Benjamin-Ono equation is successfully employed. In the same vein, also the new ()-dimensional Benjamin-Ono equation to ()-dimensional spaces is extended and then analyzed and investigated. Different forms of exact solitary wave solutions to this new equation were also determined. Graphical illustrations for certain solutions in both equations are provided. We alternatively offer that the determining method is general, impressive, outspoken, and powerful and can be exerted to create exact solutions of various kinds of nonlinear models originated in mathematical physics and engineering.

中文翻译：

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关于Benjamin-Ono方程新（）和（）维扩展的精确孤波解

本文使用Kudryashov方法为新开发的（）维本杰明-奥诺方程已成功应用。同样，新的（）-（）维空间被扩展，然后进行分析和研究。还确定了该新方程的不同形式的精确孤立波解。提供了两个方程式中某些解决方案的图形说明。或者，我们提出确定方法是通用的，令人印象深刻，直言不讳且功能强大的，可用于创建源自数学物理学和工程学的各种非线性模型的精确解。