From nonassociativity to solutions of the KP hierarchy
arXiv:nlin/0608017 · doi:10.1007/s10582-006-0412-z
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.
arXiv comment7 pages, 4 figures, International Colloquium 'Integrable Systems and Quantum Symmetries', Prague, 15-17 June 2006
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