Lump solutions and bilinear Bäcklund transformation for the $$(4+1)$$ ( 4 + 1 ) -dimensional Fokas equation

The $$(4+1)$$ -dimensional Fokas (4DFK) equation is explicitly written out by means of the linearized operator of the 4DFK equation after introducing an additional auxiliary variable. Based on the bilinear form, bilinear Backlund transformations consisting of three bilinear equations are provided. A new class of lump solutions is given and analyzed using the extremum theory of multivariate function, of which the peculiar dynamic property is demonstrated graphically.