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Nonassociativity and Integrable Hierarchies | | Aristophanes Dimakis
; Folkert Muller-Hoissen
; | | Date: |
31 Dec 2005 | | Subject: | Exactly Solvable and Integrable Systems | | Abstract: | We show that a simple nonassociative algebra is at work in the combinatorics underlying the structure of differential equations of some integrable hierarchies (like `noncommutative’ Burgers and KP). This suggests a certain weakly nonassociative algebra as a unifying framework for (a possibly restricted class of) integrable systems. We construct a `nonassociative hierarchy’ as a consequence of which several familiar integrable hierarchies emerge. As a byproduct we obtain a `noncommutative’ (e.g., matrix) version of the differential Fay identity for the KP hierarchy. | | Source: | arXiv, nlin/0601001 | | Services: | Forum | Review | PDF | Favorites | |
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