Painlevé Ping-Pong P3-P5
In this lecture I should like to discuss the concept of the Ping-Pong which appeared in the Painlevé equations. First let me explain that the name “Painlevé Ping-Pong”, in this context, is not mine but belongs to Prof. F. J. Bureau . In the first part of my talk I shall give the explicit construction of this Ping-Pong for the third and fifth Painlevé equations. The Ping-Pong, fairly sketchily, is a special kind of the transformation and exists also for the other Painlevé equations [1,2]. It can be considered as the Bäcklund transformation for the third and fifth Painlevé equations . In the second part I shall describe the possible physical applications of this Ping-Pong.
KeywordsIsing Model Higgs Field Fourth Component Dimensional Ising Model Painlev6 Equation
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- F. J. Bureau, private communication.Google Scholar
- Z. Popowicz, The Bäcklund transformations for the third and fifth Painlevé equations, IFT University of Wroclaw preprint (1982).Google Scholar
- N. Lukashevich, Differential Equations 3, 11 (1967); in Russian: 1913, (1967).Google Scholar
- V. Gromak, Differential Equations 9, 2–373 (1975).Google Scholar
- T. T. Wu, B. M. McCoy, C. A. Tracy, and E. Barouch, Spin-spin correlation functions for the twodimensional Ising model: exact theory in the scaling region. Phys. Rev. B13, 318–374 (1976).Google Scholar
- M. A. Lohe, Two-and three-dimensional instantons. Phys. Lett. 70B, 325–328 (1977).Google Scholar
- E. B. Bogomol'nyî, The stability of classical solutions. Soviet J. Nucl. Phys. 24, 449–454 (1976).Google Scholar
- M. K. Prasad and C. M. Sommerfeld, Exact classical solution for the't Hooft monopole and the Julia-Zee dyon. Phys. Rev. Lett. 35, 760–762 (1975).Google Scholar