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

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##### Citation

Dimakis, A., & Müller-Hoissen, F. (2006). From nonassociativity to solutions of
the KP hierarchy.* Czechoslovak Journal of Physics,* *56*,
1123-1130. doi:10.1007/s10582-006-0412-z.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0029-1527-F

##### 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.