Multi-solutions with specific geometrical wave structures to a nonlinear evolution equation in the presence of the linear superposition principle

Abstract

Abstract Lump solutions are one of the most common solutions for nonlinear evolution equations. This study aspires to investigate the generalized Hietarintatype equation. We auspiciously provide multiple M-lump waves. On the other hand, collision phenomena to multiple M-lump waves with soliton wave solutions are also provided. During the collision, the amplitude of the lump will change significantly over the processes, whereas the amplitude of the soliton will just minimally alter. As it is of paramount importance, we use suitable values of parameter to put out the physical features of the reported results through three dimensional and contour graphics. The results presented express physical features of lump and lump interaction phenomena of different kinds of nonlinear physical processes. Further, this study serves to enrich nonlinear dynamics and provide insight into how nonlinear waves propagate.