Higher dimensional Painlevé integrable models from the real nonlinear evolution equations
Higher dimensional Painlevé integrable models from the real nonlinear evolution equations
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DOI：
10.1088/1009-1963/10/2/301
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发表时间：
2001-02
期刊：
影响因子：
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通讯作者：
H. Ruan;Yi-Xin Chen
中科院分区：
文献类型：
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作者：
H. Ruan;Yi-Xin Chen
提出了一种共形不变渐近展开方法来求解任何维度的非线性可积和不可积模型。可以同时获得许多具有相同尺寸的新 Painlevé 可积模型。以(2+1)维KdV-Burgers(KdVB)方程和(3+1)维Zabolotskaya-Khokhlov和Kudomtsev-Petviashvili(ZKKP)方程为例，我们得到了一些新的具有Painlevé性质的高维共形不变量模型以及这些模型的近似解。在某些特殊情况下，一些近似解会变得精确。
A conformal invariant asymptotic expansion approach is proposed to solve any nonlinear integrable and nonintegrable models with any dimension. Many new Painlevé 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 Painlevé property and the approximate solutions of these models. In certain special cases, some of the approximate solutions become exact.