The Isomonodromic Deformation Method in the Theory of Painlevé Equations

Introduction....Pages 1-14
Monodromy data for the systems of linear ordinary differential equations with rational coefficients....Pages 15-37
Isomonodromic deformations of systems of linear ordinary differential equations with rational coefficients....Pages 38-42
Isomonodromic deformations of systems (1.9) and (1.26) and painlevé equations of II and III types....Pages 43-45
Inverse problem of the monodromy theory for the systems (1.9) and (1.26). Asymptotic analysis of integral equations of the inverse problem....Pages 46-61
Asymptotic solution to a direct problem of the monodromy theory for the system (1.9)....Pages 62-79
Asymptotic solution to a direct problem of the monodromy theory for the system (1.26)....Pages 80-86
The manifold of solutions of painlevé II equation decreasing as χ → −∞. Parametrization of their asymptotics through the monodromy data. Ablowitz-segur connection formulae for real-valued solutions decreasing exponentially as χ → + ∞ ....Pages 87-93
The manifold of solutions to painlevé III equation. The connection formulae for the asymptotics of real-valued solutions to the cauchy problem....Pages 94-108
The manifold of solutions to painlevé II equation increasing as χ → + ∞ . The expression of their asymptotics through the monodromy data. The connection formulae for pure imaginary solutions....Pages 109-123
The movable poles of real-valued solutions to painlevé II equation and the eigenfunctions of anharmonic oscillator....Pages 124-146
The movable poles of the solutions of painlevé III equation and their connection with mathifu functions....Pages 147-172
Large-time asymptotics of the solution of the cauchy problem for MKdV equation....Pages 173-204
The dynamics of electromagnetic impulse in a long laser amplifier....Pages 205-211
The scaling limit in two-dimensional ising model....Pages 212-215
Quasiclassical mode of the three-dimensional wave collapse....Pages 216-229