2 N line-soliton solutions of the (2+1)-dimensional Kadomtsev–Petviashvili equation can be presented by resorting to the Hirota bilinear method. By extending the real parameters into complex parameters, this paper obtains N periodic-soliton solutions of the (2+1)-dimensional Kadomtsev–Petviashvili equation from the 2N line-soliton solutions.
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Zhaqilao et al. (2008) studied this question.