From nonassociativity to solutions of the KP hierarchy

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.Comment: 7 pages, 4 figures, International Colloquium 'Integrable Systems and Quantum Symmetries', Prague, 15-17 June 200