A note on the Lax pairs for Painlevé equations

Journal of Physics A: Mathematical and General

Volumn 32, Issue 46, 1999, Pages 8145-8156

  Kapaev, A A ^a   Hubert, E ^b  

^a STEKLOV MATHEMATICAL INSTITUTE   (Russian Federation)

^b MATHEMATICAL SCIENCES RESEARCH INSTITUTE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033584754     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/32/46/311     Document Type: Article

References (28)

1. Painlevé P 1900 Mémoire sur les équations differentielles dont l'integrale générale est uniforme Bull. Soc. Math. France. 28 201-61
2. Gambier B 1910 Sur les équations differentielles du second ordre et du premier degré dont l'integrale générale est a points critiques fixes Acta Math. 33 1-55
3. Ince E L 1959 Ordinary Differential Equations (New York: Dover)
4. Fuchs R 1907 Über lineare homogene Differentialgleichungen zweiter Ordnung mit drei im Endlichen gelegenen wesentlich singulären Stellen Math. Annalen 63 301-21
5. Painlevé P 1906 Sur les équations differentielles du second ordre à points critiques fixes Comptes Rendus 143 1111-17
6. Garnier R 1912 Sur les équationes différentielles du troisième ordre dont l'intégrale générale est uniforme et sur une classe d'èquationnes nouvelles d'ordre supérieur dont l'intégrale générale a ses points critique fixes Ann. Sci. Ec. Norm. Super. 29 1-126
7. Boutroux P 1913 Recherches sur les transcendantes de M Painlevé et l'étude asymptotique des équationes différentielle du second ordre Ann. Sci. Ec. Norm. Super. 31 99-159
8. Jimbo M and Miwa T 1981 Monodromy preserving deformation of linear ordinary differential equations with rational coefficients II Physica D 2 407-48
9. Its A R, Kapaev A A and Kitaev A V 1988 The isomonodromic deformation method and special functions Problems of Theoretical Physics vol III, ed Yu N Demkov, Yu V Novozhilov and P P Pavinsky (Leningrad: Leningrad State University Press) pp 182-92
10. Bateman H and Erdélyi A 1953 Higher Transcendental Functions (New York: McGraw-Hill)
11. Its A R, Izergin A G, Korepin V E and Slavnov N A 1990 Differential equations for quantum correlation functions Int. J. Mod. Phys. B 4 1003-37 Its A R, Izergin A G, Korepin V E and Slavnov N A 1993 The quantum correlation function as the τ function of classical differential equations Important Developments in Soliton Theory eds A S Fokas and V E Zakharov (Berlin: Springer) pp 407-17
12. Its A R, Izergin A G, Korepin V E and Slavnov N A 1990 Differential equations for quantum correlation functions Int. J. Mod. Phys. B 4 1003-37 Its A R, Izergin A G, Korepin V E and Slavnov N A 1993 The quantum correlation function as the τ function of classical differential equations Important Developments in Soliton Theory eds A S Fokas and V E Zakharov (Berlin: Springer) pp 407-17
13. Tracy C A and Widom H 1994 Fredholm determinants, differential equations and matrix models Commun. Math. Phys. 163 33-72 Tracy C A and Widom H 1999 Fredholm determinants, differential equations and matrix models PBB: xxx.lanl.gov hepth/9306042 v3 2 Feb
14. Tracy C A and Widom H 1994 Fredholm determinants, differential equations and matrix models Commun. Math. Phys. 163 33-72 Tracy C A and Widom H 1999 Fredholm determinants, differential equations and matrix models PBB: xxx.lanl.gov hepth/9306042 v3 2 Feb
15. Deift P 1999 Integrable operators Differential Operators and Spectral Theory (M Sh. Birman's 70th Anniversary Collection) (AMS Translations, Advances in the Mathematical Sciences 41) vol 189, ed V Buslaev, M Solomyak and D Yafaev, pp 69-84
16. Bleher P, Bolibrukh A, Its A and Kapaev A, Linearization of P34 equation of Painlevé-Gambier, in preparation
17. Jimbo M, Miwa T, Môri Y and Sato M 1980 Density matrix of an impenetrable Bose gas and the fifth Painlevé transcendent Physica D 1 80-158
18. Mehta M L 1991 Random Matrices 2nd edn (San Diego: Academic)
19. Tracy C A and Widom H 1994 Level-spacing distributions and the Airy kernel Commun. Math. Phys. 159 151-74
20. Tracy C A and Widom H 1994 Level-spacing distributions and the Bessel kernel Commun. Math. Phys. 161 289-309
21. Muskhelishvili N I 1953 Singular Integral Equations 2nd edn (Groningen: Noordhoff)
22. Hubert E Factorization free decomposition algorithms in differential algebra J. Symbolic Comput. to appear
23. Flaschka H and Newell A C 1980 Monodromy-and spectrum preserving deformations I Commun. Math. Phys. 76 67-116
24. Gromak V I 1975 Theory of Painlevé's equation Diff. Uravnen. 11 373-6
25. Kitaev A V 1985 On the self-similar solutions of the modified nonlinear Schrödinger equation Teor. Mat. Fizika 64 347-69
26. Milne A E, Clarkson P A and Bassom A P 1997 Application of the isomonodromy deformation method to the fourth Painlevé equation Inverse Problems 13 421-39
27. Kaup D J and Newell A C 1978 An exact solution for a derivative nonlinear Schrödinger equation J. Math. Phys. 19 798-801
28. Ablowitz M J, Ramani A and Segur H 1980 A connection between nonlinear evolution equations and ordinary differential equations of p-type J. Math. Phys. 21 1006-15