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Communications in Mathematical Physics

, Volume 203, Issue 3, pp 649–666 | Cite as

Riccati-Type Equations, Generalised WZNW Equations, and Multidimensional Toda Systems

  • L. A. Ferreira
  • J. F. Gomes
  • A. V. Razumov
  • M. V. Saveliev
  • A. H. Zimerman

Abstract:

We associate to an arbitrary ℤ-gradation of the Lie algebra of a Lie group a system of Riccati-type first order differential equations. The particular cases under consideration are the ordinary Riccati and the matrix Riccati equations. The multidimensional extension of these equations is given. The generalisation of the associated Redheffer–Reid differential systems appears in a natural way. The connection between the Toda systems and the Riccati-type equations in lower and higher dimensions is established. Within this context the integrability problem for those equations is studied. As an illustration, some examples of the integrable multidimensional Riccati-type equations related to the maximally nonabelian Toda systems are given.

Keywords

Differential Equation High Dimension Differential System Riccati Equation Order Differential Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • L. A. Ferreira
    • 1
  • J. F. Gomes
    • 1
  • A. V. Razumov
    • 2
  • M. V. Saveliev
    • 2
  • A. H. Zimerman
    • 1
  1. 1.Instituto de Física Teórica - IFT/UNESP, Rua Pamplona 145, 01405-900, São Paulo - SP, Brazil.¶E-mail: laf@ift.unesp.br; jfg@ift.unesp.br; zimerman@ift.unesp.brBR
  2. 2.Institute for High Energy Physics, 142284 Protvino, Moscow Region, Russia.¶ E-mail: razumov@mx.ihep.su; saveliev@mx.ihep.suSU

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