The isomonodromic deformation method in the theory of Painlevé equations
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Bibliographic Information
The isomonodromic deformation method in the theory of Painlevé equations
（Lecture notes in mathematics, 1191）
Springer-Verlag, c1986
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- : us
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Library & Science Information Center, Osaka Prefecture University
: gwNDC8:410.8||||10009465465
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
L/N||LNM||11918609033S
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Note
Bibliography: p. [307]-311
Includes index
"Subseries: USSR"
Description and Table of Contents
Table of Contents
Monodromy data for the systems of linear ordinary differential equations with rational coefficients.- Isomonodromic deformations of systems of linear ordinary differential equations with rational coefficients.- Isomonodromic deformations of systems (1.9) and (1.26) and painleve equations of II and III types.- Inverse problem of the monodromy theory for the systems (1.9) and (1.26). Asymptotic analysis of integral equations of the inverse problem.- Asymptotic solution to a direct problem of the monodromy theory for the system (1.9).- Asymptotic solution to a direct problem of the monodromy theory for the system (1.26).- The manifold of solutions of painleve II equation decreasing as ? ? ??. Parametrization of their asymptotics through the monodromy data. Ablowitz-segur connection formulae for real-valued solutions decreasing exponentially as ? ? + ?.- The manifold of solutions to painleve III equation. The connection formulae for the asymptotics of real-valued solutions to the cauchy problem.- The manifold of solutions to painleve II equation increasing as ? ? + ?. The expression of their asymptotics through the monodromy data. The connection formulae for pure imaginary solutions.- The movable poles of real-valued solutions to painleve II equation and the eigenfunctions of anharmonic oscillator.- The movable poles of the solutions of painleve III equation and their connection with mathifu functions.- Large-time asymptotics of the solution of the cauchy problem for MKdV equation.- The dynamics of electromagnetic impulse in a long laser amplifier.- The scaling limit in two-dimensional ising model.- Quasiclassical mode of the three-dimensional wave collapse.
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