Hamiltonian theory over noncommutative rings and integrability in multidimensions
Hamiltonian theory over noncommutative rings and integrability in multidimensions
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DOI：
10.1063/1.529621
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发表时间：
1992-07
影响因子：
1.3
通讯作者：
I. Dorfman;A. Fokas
中科院分区：
文献类型：
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作者：
I. Dorfman;A. Fokas
利用Adler-Gel 'fand-Dikii格式的推广，在两个空间维度上生成双哈密顿结构。为了实现该方案，在非交换环上建立了哈密顿理论，即形式伪微分算子环。以这种方式生成的双哈密顿结构可以用于Kadomtsev-Petviashvili方程以及2+1中的其他可积方程。
A generalization of the Adler–Gel’fand–Dikii scheme is used to generate bi‐Hamiltonian structures in two spatial dimensions. In order to implement this scheme, a Hamiltonian theory is built over a noncommutative ring, namely the ring of formal pseudodifferential operators. Bi‐Hamiltonian structures generated in this way can be used for the Kadomtsev–Petviashvili equation as well as other integrable equations in 2+1.