Padé Methods for Painlevé Equations - Hidehito Nagao, Yasuhiko Yamada

Padé Methods for Painlevé Equations

Buch | Softcover
90 Seiten
2021 | 1st ed. 2021
Springer Verlag, Singapore
978-981-16-2997-6 (ISBN)
69,54 inkl. MwSt
The isomonodromic deformation equations such as the Painlevé and Garnier systems are an important class of nonlinear differential equations in mathematics and mathematical physics. In choosing the suitable approximation problem, the linear differential equations give the Lax pair for some isomonodromic equations.
The isomonodromic deformation equations such as the Painlevé and Garnier systems are an important class of nonlinear differential equations in mathematics and mathematical physics. For discrete analogs of these equations in particular, much progress has been made in recent decades. Various approaches to such isomonodromic equations are known: the Painlevé test/Painlevé property, reduction of integrable hierarchy, the Lax formulation, algebro-geometric methods, and others. Among them, the Padé method explained in this book provides a simple approach to those equations in both continuous and discrete cases.
For a given function f(x), the Padé approximation/interpolation supplies the rational functions P(x), Q(x) as approximants such as f(x)~P(x)/Q(x). The basic idea of the Padé method is to consider the linear differential (or difference) equations satisfied by P(x) and f(x)Q(x). In choosing the suitable approximation problem, the linear differential equations give the Lax pair for some isomonodromic equations. Although this relation between the isomonodromic equations and Padé approximations has been known classically, a systematic study including discrete cases has been conducted only recently. By this simple and easy procedure, one can simultaneously obtain various results such as the nonlinear evolution equation, its Lax pair, and their special solutions. In this way, the method is a convenient means of approaching the isomonodromic deformation equations.

1Padé approximation and di erential equation.- 2Padé approximation for Pvi.- 3Padé approximation for q-Painlevé/Garnier equations.- 4Padé interpolation.- 5Padé interpolation on q-quadratic grid.- 6Multicomponent Generalizations.

“The monograph under review explores an important connection between integrable systems and approximation theory: the appearance of integrable systems in Padé approximation and interpolation problems. Both authors have contributed plenty of work in this direction together and individually, and one can view this work as a pedagogical guide to this rich area. … The monograph is well organized, and has plenty of examples motivating the discussion and demonstrating the power of the Padé method … .” (Ahmad Bassam Barhoumi, Mathematical Reviews, September, 2022)

Erscheinungsdatum
Reihe/Serie SpringerBriefs in Mathematical Physics ; 42
Zusatzinfo 1 Illustrations, color; 1 Illustrations, black and white; VIII, 90 p. 2 illus., 1 illus. in color.
Verlagsort Singapore
Sprache englisch
Maße 155 x 235 mm
Themenwelt Mathematik / Informatik Mathematik Analysis
Naturwissenschaften Physik / Astronomie Theoretische Physik
ISBN-10 981-16-2997-8 / 9811629978
ISBN-13 978-981-16-2997-6 / 9789811629976
Zustand Neuware
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