Finite‐order meromorphic solutions and the discrete Painlevé equations
Finite‐order meromorphic solutions and the discrete Painlevé equations
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DOI：
10.1112/plms/pdl012
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发表时间：
2005-04
影响因子：
1.8
通讯作者：
R. Halburd;R. Korhonen
中科院分区：
文献类型：
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作者：
R. Halburd;R. Korhonen
设w(Z)是二阶差分方程w(z+1)+w(z−1)=R(z，w(Z))的可容许有限阶亚纯解，其中R(z，w(Z))在w(Z)中是有理的，且系数在z中是亚纯的，则w(Z)满足差分线性方程或Riccati方程，否则上述方程可转化为一系列典型差分方程组之一.该列表包括上述形式的所有已知的差分Painlevé方程及其自治版本。这表明有限阶亚纯解的存在是可积差分方程解的一个很好的检测器。
Let w(z) be an admissible finite‐order meromorphic solution of the second‐order difference equation w(z+1)+w(z−1)=R(z,w(z)) where R(z, w(z)) is rational in w(z) with coefficients that are meromorphic in z. Then either w(z) satisfies a difference linear or Riccati equation or else the above equation can be transformed to one of a list of canonical difference equations. This list consists of all known difference Painlevé equations of the above form, together with their autonomous versions. This suggests that the existence of finite‐order meromorphic solutions is a good detector of integrable difference equations.