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Integrable hierarchies: Painlevé indices and compatibility conditions

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Abstract

We consider the application of the Weiss-Tabor-Carnevale (WTC) Painlevé test to hierarchies of completely integrable evolution equations. A method of constructing the Painlevé index polynomial for such hierarchies is illustrated. For Burgers' hierarchy we are able to show that all WTC compatibility conditions are satisfied. This allows a simple construction of the Painlevé-Bäcklund transformation obtained from truncation of the principal Painlevé expansion.

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Authors
  1. A. Pickering
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Additional information

Department of Mathematics, Heriot-Watt University, Edinburgh EH14 4AS, United Kingdom. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 99, No. 3, pp. 509–516, June, 1994.

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Pickering, A. Integrable hierarchies: Painlevé indices and compatibility conditions. Theor Math Phys 99, 761–766 (1994). https://doi.org/10.1007/BF01017065

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  • DOI: https://doi.org/10.1007/BF01017065

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