Justification of the asymptotic formulas obtained by the isomonodromic deformation method. (English. Russian original) Zbl 0745.34061

Kitaev, A. V.

J. Sov. Math. 57, No. 3, 3131-3135 (1991); translation from Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 179, 101-109 (1989).

See the review in Zbl 0708.34059.

MSC:

34E99

Asymptotic theory for ordinary differential equations

Keywords:

differential equations of the Painlevé type; isomonodromic deformation method

Citations:

Zbl 0708.34059

References:

[1]	H. Flashka and A. C. Newell, ?Monodromy and spectrum-preserving deformations. I,? Comm. Math, Phys.,76, No. 1, 67?116 (1980).
[2]	M. Jimbo and T. Miwa, ?Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. I,? Physica D,2, No. 2, 306?352 (1981). · Zbl 1194.34167
[3]	M. Jimbo and T. Miwa, ?Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. II,? Physica D,2, No. 3, 407?448 (1981). · Zbl 1194.34166
[4]	M. Jimbo and T. Miwa, ?Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. III,? Physica D,4, No. 1, 26?46 (1981). · Zbl 1194.34169
[5]	A. R. Its and V. Yu. Novokshenov, The Isomonodromic Deformation Method in the Theory of Painlevé Equations, Lecture Notes in Math., Vol. 1191, Springer-Verlag, Berlin-New York (1986). · Zbl 0592.34001
[6]	B. M. McCoy and Sh. Tang, ?Connection formulae for Painlevé Y functions,? Physica D,19, No. 1, 42?72 (1986). · Zbl 0639.58041
[7]	B. M. McCoy and Sh. Tang, ?Connection formulae for Painlevé Y functions II. The (?-function Bose gas problem,? Physica D,20, No. 1, 187?216 (1986). · Zbl 0656.35114
[8]	A. P. Its and A. A. Kapaev, ?The isomonodromic deformation method and connection formulas for the second Painlevé transcendent,? Izv. Akad. Nauk SSSR Ser. Mat.,51, No. 4, 878?892 (1987). · Zbl 0681.34053
[9]	A. V. Kitaev, ?The isomonodromic deformation method and asymptotic formulas for the solutions of the?complete? third Painlevé equation,? Mat. Sb.,134(176), No. 3(11), 421?444 (1987).
[10]	A. S. Abdullaev, ?To the theory of Painlevé’s second equation,? Dokl. Akad. Nauk SSSR,273, No. 5, 1033?1036 (1983).
[11]	A. S. Abdullaev, ?The asymptotics of the solutions of the generalized sine-Gordon equation, Painlevé’s third equation, and d’Alembert’s equation,? Dokl. Akad. Nauk SSSR,280, No. 2, 265?268 (1985). · Zbl 0612.35115
[12]	B. I. Suleimanov, ?Connection between the asymptotic formulas for various infinities for the solution of Painlevé’s second equation,? Differentsial’nye Uravneniya,23, No. 5, 834?842 (1987).
[13]	H. Kimura, ?The construction of a general solution of a Hamiltonian system with regular type singularity,? Ann. Mat. Pura Appl. Ser. Quarta,134, 363?392 (1983). · Zbl 0532.70013
[14]	K. Takano, ?A 2-parameter family of solutions of Painlevé equation (Y) near the point at infinity,? Funksial. Ekvac.,26, No. 1, 79?113 (1983).
[15]	P. Boutroux, ?Recherches sur les transcendantes de M. Painlevé et l’etude asymptotique des équations différentielles,? Ann. Sci. École Norm. Sup.,30, 255?376 (1913). · JFM 44.0382.02
[16]	P. Boutroux, ?Recherches sur les transcendantes de M. Painlevé et l’etude asymptotique des équations différentielles,? Ann. Sci. École Norm. Sup.,31, 99?159 (1914). · JFM 45.0478.02
[17]	S. P. Hastings and J. B. McLeod, ?Boundary value problem associated with the second Painlevé transcendent and the Korteweg-de Vries equation,? Arch. Rational Mech. Anal.,73, 31?51 (1980). · Zbl 0426.34019
[18]	A. S. Fokas, U. Mugan, and M. J. Ablovitz, ?A method of solution for Painlevé equations: Painlevé IV, Y,? Preprint INS, No. 73, Clarkson Univ., New York-Potsdam (1987).