HIGHER-DIMENSIONAL PAINLEVE INTEGRABLE MODELS FROM THE KADOMTSEV-PETVIASHVILI EQUATION

After embedding the Kadomtsev-Petviashvili equation in higher dimensio ns and extending the Painleve analysis approach to a new form such tha t the coefficients of the expansion around the singular manifold posse ss conformal invariance and contain explicit new space variables, we c an get infinitely many Painleve' integrable models in (3+1)-dimensions and higher dimensions. Some concrete higher dimensional modified Kort eweg-de Vries type of extensions are given. Whether the models are Lax integrable or integrable under other meanings remain still open. (C) 1998 American Institute of Physics. [S0022-2488(98)00510-6].