Variants of a (3+1)-dimensional generalized BKP equation: Multiple-front waves solutions

•We investigate three variants of the BKP equation.•We derive distinct dispersion relation for each variant.•We derive multiple-front wave solutions for each variant.

The simplified form of the Hirota’s method is used to investigate three variants of a (3+1)-dimensional generalized BKP equation. Multiple-front wave solutions are formally derived. The dispersion relation and the phase shift of each equation are established. The constraints, that arise between the coefficients of the spatial variables, that will guarantee the existence of multiple solutions, are analyzed.