HIGHER DIMENSIONAL PAINLEVé INTEGRABLE MODELSWITH REAL PHYSICAL SIGNIFICATION

A “M?bius” 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 Kudomtsev-Petviashvili (KP) equation as concrete examples, we obtain some new higher dimensional “M?bius” invariant models with Painlevé property and the approximate solutions of these models. In some special case, some approximate solutions become exact.