Abstract
•Abundant periodic wave solutions for fifth-order Sawada-Kotera equations was constructed.•The solutions of these models were found using Hirota’s bilinear algorithm.•The acquired solutions are elucidated by 3D figures and some contour plots.
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.