A cubic Hamiltonian system with meromorphic solutions

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A Hamiltonian system in two dependent variables is presented with properties analogous to the Hamiltonian systems associated with the six Painlevé equations. Its solutions are meromorphic functions in the complex plane having only simple poles with three possible residues given by the third roots of unity. Like the Painlevé equations PI - PVI the system has families of rational solutions that can be obtained by applying Bäcklund transformations to certain seed solutions.
Original languageEnglish
Pages (from-to)307-317
JournalComputational Methods and Function Theory
Issue number2
Early online date27 Oct 2015
Publication statusPublished - Jun 2016


  • Hamiltonian system
  • meromorphic solution
  • Painleve equations
  • Bäcklund transformation


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