Second-degree Painlevé equations and their contiguity relations

Basil Grammaticos, Alfred Ramani, Partha Guha

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


We study second-order, second-degree systems related to the Painlevé equations which possess one and two parameters. In every case we show that by introducing a quantity related to the canonical Hamiltonian variables it is possible to derive such a second-degree equation. We investigate also the contiguity relations of the solutions of these higher-degree equations. In most cases these relations have the form of correspondences, which would make them non-integrable in general. However, as we show, in our case these contiguity relations are indeed integrable mappings, with a single ambiguity in their evolution (due to the sign of a square root).

Original languageBritish English
Pages (from-to)37-47
Number of pages11
JournalRegular and Chaotic Dynamics
Issue number1
StatePublished - Feb 2014


  • contiguity relations
  • Hamiltonian formalism
  • Painlevé equations
  • second-degree differential equations


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