THE PAINLEVE PROPERTY FOR PARTIAL DIFFERENTIAL EQUATIONS. II. BACKLUND TRANSFORMATION, LAX PAIRS, AND THE SCHWARZIAN DERIVATIVE
THE PAINLEVE PROPERTY FOR PARTIAL DIFFERENTIAL EQUATIONS. II. BACKLUND TRANSFORMATION, LAX PAIRS, AND THE SCHWARZIAN DERIVATIVE
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DOI：
10.1063/1.525875
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发表时间：
1983-06
影响因子：
1.3
通讯作者：
J. Weiss
中科院分区：
文献类型：
--
作者：
J. Weiss
本文研究了偏微分方程的Painleve性质。通过对几个著名的偏微分方程（Burgers, KdV, MKdV, Bousinesq，高阶KdV和KP方程）的应用表明，考虑“奇异流形”可以用“施瓦兹导数”来表示这些方程。这个公式在Moebius群（作用于因变量）下是不变的，并被证明可以得到相应的Lax对（线性化）。
In this paper we investigate the Painleve property for partial differential equations. By application to several well‐known partial differential equations (Burgers, KdV, MKdV, Bousinesq, higher‐order KdV and KP equations) it is shown that consideration of the ‘‘singular manifold’’ leads to a formulation of these equations in terms of the ‘‘Schwarzian derivative.’’ This formulation is invariant under the Moebius group (acting on dependent variables) and is shown to obtain the appropriate Lax pair (linearization) for the underlying nonlinear pde.