A (3+1)‐dimensional Painlevé integrable model obtained by deformation

To find some non‐trivial higher‐dimensional integrable models (especially in (3+1) dimensions) is one of the most important problems in non‐linear physics. An efficient deformation method to obtain higher‐dimensional integrable models is proposed. Starting from (2+1)‐dimensional linear wave equation, a (3+1)‐dimensional non‐trivial non‐linear equation is obtained by using a non‐invertible deformation relation. Further, the Painlevé integrability of the resulting model is also proved. Copyright © 2002 John Wiley & Sons, Ltd.