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Differential Resultant, Computer Algebra and Completely Integrable Dynamical Systems

  • Zoia Kostova
  • Nikolay Kostov
  • Vladimir Gerdjikov
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6244)

Abstract

For a pair of differential operators A and B with periodic coefficients we construct their differential resultant and derive condition for their commutativity. By considering this condition as a stationary Lax representation we are able to treat completely integrable dynamical systems. As special cases we obtain Hénon-Heiles dynamical systems. We propose algorithms to do this by using the powerful methods of computer algebra and performing symbolic calculations in Maple13 and Reduce4.

Keywords

computer algebra Lax representation Baker-Akhiezer function differential resultant algebra of commuting differential operators 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Zoia Kostova
    • 1
  • Nikolay Kostov
    • 2
  • Vladimir Gerdjikov
    • 2
  1. 1.Meridian 22 Private SchoolSofiaBulgaria
  2. 2.Institute of Nuclear Research and Nuclear EnergyBulgarian Academy of SciencesSofiaBulgaria

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