The Isomonodromic Deformation Method in the Theory of Painlevé Equations - Couverture souple

Its, Alexander R.; Novokshenov, Victor Y.

Couverture souple

ISBN 10 : 3540164839 ISBN 13 : 9783540164838

Editeur : Springer, 2009

Synopsis

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.

A propos du livre

À propos de la quatrième de couverture

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 painlev¿quations 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 painlev¿I 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 painlev¿II equation. The connection formulae for the asymptotics of real-valued solutions to the cauchy problem.- The manifold of solutions to painlev¿I 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 painlev¿I equation and the eigenfunctions of anharmonic oscillator.- The movable poles of the solutions of painlev¿II 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.

Détails de l'édition

• Éditeur: Springer
• Date d'édition: 2009
• Langue: anglais
• ISBN 10: 3540164839
• ISBN 13: 9783540164838
• Reliure: Broché
• Nombre de pages: 314
• Coordonnées du fabricant: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3; Heidelberg; 69115; Allemagne