HIGHER DIMENSIONAL PAINLEVé INTEGRABLE MODELS FROM THE REAL NONLINEAR EVOLUTION EQUATIONS

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