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Integrable ordinary differential equations on free associative algebras

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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.

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Authors and Affiliations

  1. Applied Mathematics Department, University of Leeds, Leeds, UK

    A. V. Mikhailov

  2. Center for Nonlinear Research, Landau Institute of Theoretical Physics, RAS, Moscow, Russia

    A. V. Mikhailov & V. V. Sokolov

Authors
  1. A. V. Mikhailov
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  2. V. V. Sokolov
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 122, No. 1, pp. 88–101, January, 1999.

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Mikhailov, A.V., Sokolov, V.V. Integrable ordinary differential equations on free associative algebras. Theor Math Phys 122, 72–83 (2000). https://doi.org/10.1007/BF02551171

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  • DOI: https://doi.org/10.1007/BF02551171

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