On matrix Painlevé hierarchies
On matrix Painlevé hierarchies
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DOI：
10.1016/j.jde.2016.03.033
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发表时间：
2016-07
影响因子：
2.4
通讯作者：
P. R. Gordoa;A. Pickering;Z. N. Zhu
中科院分区：
文献类型：
--
作者：
P. R. Gordoa;A. Pickering;Z. N. Zhu
We define a matrix first Painlevé hierarchy and a matrix second Painlevé (P II) hierarchy. For our matrix P II hierarchy we also give auto-Bäcklund transformations and consider the iteration of solutions. This is the first paper to define matrix Painlevé hierarchies and to give auto-Bäcklund transformations for a matrix Painlevé hierarchy. We also consider, amongst other results, the derivation of sequences of special integrals and autonomous limits. Until now it has been unknown how to connect the known matrix P II equation to the obvious candidates for related completely integrable matrix partial differential equations. Our matrix P II hierarchy is placed firmly within the context of a matrix modified Korteweg–de Vries (mKdV) hierarchy. In deriving our matrix P II hierarchy we make use of the Hamiltonian structure of this matrix mKdV hierarchy. We thus see once again the importance for Painlevé hierarchies of the integrability structures of related completely integrable equations.
