Differential–difference equations associated with the fractional Lax operators
Differential–difference equations associated with the fractional Lax operators
复制标题
与分数 Lax 算子相关的微分差分方程
DOI：
10.1088/1751-8113/44/41/415203
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
V. V. Postnikov
中科院分区：
文献类型：
--
作者：
V E Adler;V. V. Postnikov
我们研究了形式为Pψ = λQψ的谱问题的可积层次，其中P和Q是差分算子。相应的非线性微分-差分方程可以看作是bogoyavlensky型格的非齐次推广。当后者在连续极限下变成Korteweg-de Vries方程时，所考虑的格提供了Sawada-Kotera和kap - kupershmidt方程的离散类似物。给出了r-矩阵公式和几个最简单的显式解。
We study integrable hierarchies associated with spectral problems of the form Pψ = λQψ, where P and Q are difference operators. The corresponding nonlinear differential–difference equations can be viewed as inhomogeneous generalizations of the Bogoyavlensky-type lattices. While the latter turn into the Korteweg–de Vries equation under the continuous limit, the lattices under consideration provide discrete analogs of the Sawada–Kotera and Kaup–Kupershmidt equations. The r-matrix formulation and several of the simplest explicit solutions are presented.