Lie symmetry analysis and invariant solutions for the (3+1)-dimensional Virasoro integrable model

Lie symmetry analysis is applied to a (3+1)-dimensional Virasoro integrable model and the corresponding similarity reduction equations are obtained with the different infinitesimal generators. Invariant solutions with arbitrary functions for the (3+1)-dimensional Virasoro integrable model, including the interaction solution between a kink and a soliton, the lump-type solution and periodic solutions, have been studied analytically and graphically.