Comment on the 3+1 dimensional Kadomtsev-Petviashvili equations

We comment on traveling wave solutions and rational solutions to the 3+1 dimensional Kadomtsev-Petviashvili (KP) equations: (u(t) + 6uu(x) + u(xxx))(x) +/- 3u(yy) +/- 3u(zz) = 0. We also show that both of the 3+1 dimensional KP equations do not possess the three-soliton solution. This suggests that none of the 3+1 dimensional KP equations should be integrable, and partially explains why they do not pass the Painleve test. As by-products, the one-soliton and two-soliton solutions and four classes of specific three-soliton solutions are explicitly presented. (C) 2010 Elsevier B.V. All rights reserved.