Higher dimensional painleve integrable models from the real nonlinear evolution equations

A conformal invariant asymptotic expansion approach is proposed to solve any nonlinear integrable and nonintegrable models with any dimension. Many new Painleve integrable models with the same dimensions can be obtained at the same time. Taking the (2+1)-dimensional KdV-Burgers (KdVB) equation and the (3+1)-dimensional Zabolotskaya-Khokhlov and Kudomtsev-Petviashvili (ZKKP) equation as concrete examples, we obtain some new higher dimensional conformal invariant models with a Painleve property and the approximate solutions of these models. In certain special cases, some of the approximate solutions become exact.