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From nonassociativity to solutions of the KP hierarchy | | Aristophanes Dimakis
; Folkert Muller-Hoissen
; | | Date: |
10 Aug 2006 | | Abstract: | A recently observed relation between ’weakly nonassociative’ algebras A (for which the associator (A,A^2,A) vanishes) and the KP hierarchy (with dependent variable in the middle nucleus A’ of A) is recalled. For any such algebra there is a nonassociative hierarchy of ODEs, the solutions of which determine solutions of the KP hierarchy. In a special case, and with A’ a matrix algebra, this becomes a matrix Riccati hierarchy which is easily solved. The matrix solution then leads to solutions of the scalar KP hierarchy. We discuss some classes of solutions obtained in this way. | | Source: | arXiv, nlin/0608017 | | Services: | Forum | Review | PDF | Favorites | |
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