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Journal Article

From nonassociativity to solutions of the KP hierarchy


Müller-Hoissen,  Folkert
Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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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: https://hdl.handle.net/11858/00-001M-0000-0029-1527-F
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.