Lump-type solutions and interaction solutions in the (3 + 1)-dimensional potential Yu–Toda–Sasa–Fukuyama equation

Abstract

In this work, we consider the (3 + 1)-dimensional potential Yu–Toda–Sasa–Fukuyama (YTSF) equation. By employing the extended homoclininc test approach and Hirota bilinear method, we derive a class of lump solutions of the potential YTSF equation. It is interesting that interaction solutions between the lump-type solution and one stripe soliton, and the lump-type solution and a pair of resonance solution are obtained, respectively, by using a direct method. The interaction solutions of the potential YTSF equation show that a lump-type solution appears from a soliton wave and swallowed by it later, which are the completely non-elastic interactions that rare to see. Moreover, we also obtain its periodic lump-type solutions. It is hoped that our results can be used to enrich the dynamic behaviors of the YTSF-type equations.