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)


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.


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


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© 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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