Multiple periodic-soliton solutions to Kadomtsev–Petviashvili equation

Based on the extended homoclinic test technique, we introduce two new ansätz functions to construct multiple periodic-soliton solutions of Kadomtsev–Petviashvili (KP) equation by the Hirota’s bilinear method. Some entirely new periodic-soliton solutions are obtained. The obtained results show that there exist multiple-periodic solitary waves in the different directions for the KP equation, which differ from complexiton. The employed approach is powerful and can be also applied to solve other nonlinear differential equations.