Abstract
With the aid of the direct bilinear method, the formula of N-soliton solution to the generalized (3 + 1)-dimensional Yu–Toda–Sasa–Fukuyama (gYTSF) equation is succinctly obtained. By means of long-wave limit method on 2M-soliton solutions under special parameter constraints, M-order lumps can be successfully constructed. Furthermore, the propagation orbit, velocity and extremum of the 1-order lump solutions on (x,y) plane are studied in detail. Finally, we investigate three types of hybrid solutions, which describe interaction between breathers and solitons, or between lumps and solitons or breathers. These collisions are elastic, which do not lead any changes of amplitudes, velocities and shapes of the solitons, breathers and lumps after interaction.
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