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Discrete Painlevé equations: coalescences, limits and degeneracies

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  • Ramani, A.
  • Grammaticos, B.

Abstract

Starting from the standard form of the five discrete Painlevé equations we show how one can obtain (through appropriate limits) a host of new equations which are also the discrete analogues of the continuous Painlevé equations. A particularly interesting technique is the one based on the assumption that some simplification takes place in the autonomous form of the mapping following which the deautonomization leads to a new n-dependence and introduces more new discrete Painlevé equations.

Suggested Citation

  • Ramani, A. & Grammaticos, B., 1996. "Discrete Painlevé equations: coalescences, limits and degeneracies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 228(1), pages 160-171.
    • Handle: RePEc:eee:phsmap:v:228:y:1996:i:1:p:160-171
    DOI: 10.1016/0378-4371(95)00439-4
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    References listed on IDEAS

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    1. Grammaticos, B. & Dorizzi, B., 1994. "Integrable discrete systems and numerical integrators," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 37(4), pages 341-352.
    2. Ramani, A. & Grammaticos, B. & Karra, G., 1992. "Linearizable mappings," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 180(1), pages 115-127.
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    Cited by:

    1. Sahadevan, R. & Capel, H.W., 2003. "Complete integrability and singularity confinement of nonautonomous modified Korteweg–de Vries and sine Gordon mappings," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 330(3), pages 373-390.

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