Interactional solutions of a lump and a solitary wave for two higher-dimensional equations

In this paper, by using the bilinear equation and different test functions, we obtain lump-bell solutions for the (4 + 1)-dimensional Fokas equation, which describe nonelastic and elastic interactions. We consider various interactions of the lump-bell solutions including fusion, fission, catch-up and head-on. The asymptotic behaviors and dynamics of lump-bell solutions are analyzed graphically. With a scaling transformation, we also obtain the lump-kink solution which describes elastic interactions of a lump-and a kink-type wave for the (3 + 1)-dimensional potential Yu-TodaSasa- Fukuyama equation.