Umfang:
Online-Ressource (CCCXX, 314 p, online resource)
ISBN:
9783540398233
,
9783540164838
Serie:
Lecture Notes in Mathematics 1191
Inhalt:
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 painlevé 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 painlevé 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 painlevé III equation. The connection formulae for the asymptotics of real-valued solutions to the cauchy problem -- The manifold of solutions to painlevé 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 painlevé II equation and the eigenfunctions of anharmonic oscillator -- The movable poles of the solutions of painlevé 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.
Weitere Ausg.:
ISBN 9783540164838
Weitere Ausg.:
Erscheint auch als Druck-Ausgabe Its, Alexander R. The isomonodromic deformation method in the theory of Painlevé equations Berlin : Springer, 1986 ISBN 3540164839
Weitere Ausg.:
ISBN 0387164839
Sprache:
Englisch
Fachgebiete:
Mathematik
Schlagwort(e):
Painlevé-Gleichung
;
Monodromie
URL:
Volltext
(lizenzpflichtig)
URL:
Volltext
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