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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
Article

Abstract

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.

Keywords

Local Operator Hamiltonian Operator Recursion Operator Undetermined Coefficient Free Associative Algebra 
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

© 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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