Solving the (3 + 1)-dimensional generalized KP and BKP equations by the multiple exp-function algorithm

The multiple exp-function algorithm, as a generalization of Hirota’s perturbation scheme, is used to construct multiple wave solutions to the (3+1)dimensional generalized KP and BKP equations. The resulting solutions involve generic phase shifts and wave frequencies containing many existing choices. It is also pointed out that the presented phase shifts for the two considered equations are all not of Hirota type.