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–Toda–Sasa–Fukuyama equation.