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The three-dimensional power Korteweg-de Vries equation [ut+unux+uxxx]x+uyy+uzz=0, is considered. Solitary wave solutions for any positive integer n and cnoidal wave solutions for n=1 and n=2 are obtained. The cnoidal wave solutions are shown to be represented as infinite sums of solitons by using Fourier series expansions and Poisson's summation formula.