Czechoslovak Journal of Physics

, Volume 56, Issue 10–11, pp 1123–1130 | Cite as

From nonassociativity to solutions of the KP hierarchy

  • Aristophanes Dimakis
  • Folkert Müller-Hoissen


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.


02.10.Hh 02.30.Ik 05.45.Yv 

Key words

integrable hierarchy KP nonassociativity Riccati equation soliton 


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Copyright information

© Springer 2006

Authors and Affiliations

  • Aristophanes Dimakis
    • 1
  • Folkert Müller-Hoissen
    • 2
  1. 1.Department of Financial and Management EngineeringUniversity of the AegeanChiosGreece
  2. 2.Max-Planck-Institute for Dynamics and Self-OrganizationGöttingenGermany

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