Searching for higher dimensional integrable models from lower ones via Painleve analysis

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