In this manuscript, two nonlinear fifth-order partial differential equations, namely, the bidirectional and 2D- Sawada-Kotera equations are analytically treated using an extended form of homoclinic process. In the presence of a bilinear form, novel periodic waves with different categories including periodic soliton, solitary and kinky solitary wave solutions are constructed. In the meantime, The diverse features and mechanical qualities of these acquired solutions are elucidated by 3D figures and some contour plots.

中文翻译：

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五阶Sawada-Kotera方程的丰富周期波解

在此手稿中，使用扩展形式的同宿过程对两个非线性的五阶偏微分方程（即双向方程和2D-Sawada-Kotera方程）进行了解析处理。在双线性形式的存在下，构造了具有不同类别的新型周期波，包括周期孤子，孤立和扭结孤立波解。同时，通过3D图形和一些轮廓图可以阐明这些获得的解决方案的各种功能和机械性能。