RESEARCH ARTICLE

S. V. Kovalevskaya system, its generalization and discretization

  • Matteo PETRERA ,
  • Yuri B. SURIS
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  • Institut für Mathematik, MA 7-2, Technische Universität Berlin, Str. des 17. Juni 136, 10623 Berlin, Germany

Received date: 07 Sep 2012

Accepted date: 07 Mar 2013

Published date: 01 Oct 2013

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg

Abstract

We consider an integrable three-dimensional system of ordinary differential equations introduced by S. V. Kovalevskaya in a letter to G. Mittag-Leffler. We prove its isomorphism with the three-dimensional Euler top, and propose two integrable discretizations for it. Then we present an integrable generalization of the Kovalevskaya system, and study the problem of integrable discretization for this generalized system.

Cite this article

Matteo PETRERA , Yuri B. SURIS . S. V. Kovalevskaya system, its generalization and discretization[J]. Frontiers of Mathematics in China, 2013 , 8(5) : 1047 -1065 . DOI: 10.1007/s11464-013-0305-y

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