N-solitons, lump-stripe solitons with inelastic collisions and new periodic rogue waves of a (2+1)-dimensional extended Sawada–Kotera equation

This article focuses on N-solitons and some novel multi-wave interaction phenomena of a (2+1)-dimensional extended Sawada–Kotera equation. Firstly, the bilinear form is given using a Hirota direct method, and the corresponding bilinear equation is presented from Bell polynomial theory of integrable equations. Secondly, the N-solitons of extended equation is constructed by utilizing Hirota perturbation truncation method, the obtained results are displayed in the form of stripe solitons with elastic collision. Finally, three cases of lump-stripe solitons and two new types of periodic rogue waves are obtained through a class of bilinear neural network method based on multi-layer neural network structures. Particularly, the 3D and 2D graphics are used to describe the dynamics and evolutionary collision phenomena of soliton solutions and mixed type multi-wave solutions.