Theoretical and Mathematical Physics

, Volume 122, Issue 1, pp 72–83 | Cite as

Integrable ordinary differential equations on free associative algebras

  • A. V. Mikhailov
  • V. V. Sokolov


We consider a classification problem for integrable nonlinear ordinary differential equations with an independent variable belonging to a free associative algebra M. Every equation of this type admits an m×m matrix reduction for an arbitrary m. The existence of symmetries or first integrals belonging to M is used as an integrability criterion.


Local Operator Hamiltonian Operator Recursion Operator Undetermined Coefficient Free Associative Algebra 
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Copyright information

© Kluwer Academic/Plenum Publishers 2000

Authors and Affiliations

  • A. V. Mikhailov
    • 1
    • 2
  • V. V. Sokolov
    • 2
  1. 1.Applied Mathematics DepartmentUniversity of LeedsLeedsUK
  2. 2.Center for Nonlinear Research, Landau Institute of Theoretical PhysicsRASMoscowRussia

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