From nonassociativity to solutions of the KP hierarchy

Details From nonassociativity to solutions of the KP hierarchy From nonassociativity to solutions of the KP hierarchy

2006-08-10

arxiv.org/abs/nlin/0608017v1

Nonlinear Sciences

Pattern Formation and Solitons

7 pages, 4 figures, International Colloquium 'Integrable Systems and Quantum Symmetries', Prague, 15-17 June 2006

Scientific paper

10.1007/s10582-006-0412-z

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.

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