E-Book, Englisch, Band 1191, 314 Seiten, eBook
Reihe: Lecture Notes in Mathematics
Its / Novokshenov The Isomonodromic Deformation Method in the Theory of Painleve Equations
Erscheinungsjahr 2006
ISBN: 978-3-540-39823-3
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
E-Book, Englisch, Band 1191, 314 Seiten, eBook
Reihe: Lecture Notes in Mathematics
ISBN: 978-3-540-39823-3
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
Zielgruppe
Research
Autoren/Hrsg.
Weitere Infos & Material
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.
