Asymptotic behavior of the periodic wave solution for the (3+1)-dimensional Kadomtsev–Petviashvili equation

In this paper, the one- and two-periodic wave solutions for the (3+1)-dimensional Kadomtsev–Petviashvili equation are presented by means of the Hirota’s bilinear method and the Riemann theta function. The rigorous proofs on asymptotic behaviors of these two solutions are given that soliton solution can be obtained from the periodic wave solution in an appropriate limiting procedure.