Interaction structures of (2+1)-dimensional Sawada–Kotera-like equation

Abstract

This paper mainly studies the interaction structures of lump wave and other types of localized wave for (2+ 1)-dimensional Sawada–Kotera-like (SK-Like) equation. Firstly, the $N$-soliton solutions are constructed via the Hirota bilinear method. Subsequently, using the long-wave limit method, we derive several distinct hybrid solutions which include lump-line waves, lump-breather waves, and hybrid solution among lump, line and breather waves. At the same time, we discuss that the lump wave neither collides with line waves or breather waves nor always lies on them under the conditions ${\lambda }_3=0$ and ${\lambda }_4=0$. In addition, based on the mixed solutions obtained above, by leveraging the velocity resonance mechanism, we construct the soliton molecular bound states among lump wave, line wave, and breather wave. Furthermore, through numerical simulation, vivid pictures of the superposition of lump wave and other nonlinear waves are presented.