SEARCHING FOR HIGHER-DIMENSIONAL INTEGRABLE MODELS FROM LOWER ONES VIA PAINLEVE ANALYSIS

Extending the Painleve approach to a more general form, one can get in finitely many new integrable models under the meanings that they posse ss conformal invariance and the Painleve property in any space dimensi ons from a given lower dimensional integrable model. Using the Kadomts ev-Petviashvili, nonlinear Schrodinger, and Schwarz Korteweg-de Vries equations as simple examples, some explicit (3 + 1)-dimensional integr able models are given.