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

• Received 15 September 1997

DOI:https://doi.org/10.1103/PhysRevLett.80.5027