An algebraic scheme associated with the noncommutative KP hierarchy and some of its extensions
An algebraic scheme associated with the noncommutative KP hierarchy and some of its extensions
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DOI：
10.1088/0305-4470/38/24/005
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发表时间：
2005-01
期刊：
影响因子：
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通讯作者：
A. Dimakis;F. Muller-Hoissen
中科院分区：
文献类型：
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作者：
A. Dimakis;F. Muller-Hoissen
一个著名的孤子解的anterior（'跟踪方法'）把方程的（非交换）KP层次，以及某些扩展，到家庭的代数和身份。我们开发了一个代数形式主义，特别是涉及（混合）洗牌产品，探索其结构。更确切地说，我们表明，方程的非交换KP的层次和它的扩展（xncKP）的情况下的Moyal变形的产品，在以前的工作中推导出的，对应于身份在这个代数。此外，Moyal积被更一般的结合积所取代。这导致了一个新的甚至更一般的扩展的非交换KP层次。建立了与Rota-Baxter代数的关系。
A well-known ansatz ('trace method') for soliton solutions turns the equations of the (non-commutative) KP hierarchy, and those of certain extensions, into families of algebraic sum identities. We develop an algebraic formalism, in particular involving a (mixable) shuffle product, to explore their structure. More precisely, we show that the equations of the non-commutative KP hierarchy and its extension (xncKP) in the case of a Moyal-deformed product, as derived in previous work, correspond to identities in this algebra. Furthermore, the Moyal product is replaced by a more general associative product. This leads to a new even more general extension of the non-commutative KP hierarchy. Relations with Rota–Baxter algebras are established.