Bilinear representations and lump-type waves for a fifth-order nonlinear wave equation

. In this work, we study a fifth-order nonlinear wave equation. By using the proper transformation and auxiliary parameter, two different bilinear representations are presented. We also derive a bilinear Bäcklund transformation, a Lax pair and lump-type wave solutions. The dynamics of lump-type wave solutions are investigated and exhibited mathematically and graphically. We further investigate the interaction between a kink-type solitary wave and a lump-type wave. Absorb and emit interactions between two types of solitary wave solutions are presented.