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From nonassociativity to solutions of the KP hierarchy

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Abstract

A recently observed relation between ‘weakly nonassociative’ algebras\(\mathbb{A}\) (for which the associator (\(\mathbb{A},\mathbb{A}^2 ,\mathbb{A}\)) vanishes) and the KP hierarchy (with dependent variable in the middle nucleus\(\mathbb{A}\)′ of {\(\mathbb{A}\)) 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 matrix algebra\(\mathbb{A}\)′, 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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Authors and Affiliations

  1. Department of Financial and Management Engineering, University of the Aegean, 31 Fostini Str., GR-82100, Chios, Greece

    Aristophanes Dimakis

  2. Max-Planck-Institute for Dynamics and Self-Organization, Bunsenstrasse 10, D-37073, Göttingen, Germany

    Folkert Müller-Hoissen

Authors
  1. Aristophanes Dimakis
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  2. Folkert Müller-Hoissen
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Dimakis, A., Müller-Hoissen, F. From nonassociativity to solutions of the KP hierarchy. Czech J Phys 56, 1123–1130 (2006). https://doi.org/10.1007/s10582-006-0412-z

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  • DOI: https://doi.org/10.1007/s10582-006-0412-z

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