Umfang:
1 Online-Ressource (XIV, 274 Seiten)
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Diagramme
ISBN:
9783110275667
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1283628414
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9781283628419
Serie:
De Gruyter Proceedings in Mathematics
Inhalt:
This is a proceedings of the international conference 'Painlevé Equations and Related Topics' which was taking place at the Euler International Mathematical Institute, a branch of the Saint Petersburg Department of the SteklovInstitute of Mathematicsof theRussian Academy of Sciences, in Saint Petersburg on June 17 to 23, 2011. The survey articles discuss the following topics: general ordinary differentialequations, Painlevé equations and their generalizations, Painlevé property, discrete Painlevé equations, properties of solutions of all mentioned above equations, reductions ofpartial differential equationsto Painlevé equations and their generalizations,ordinary differentialequation systems equivalent to Painlevé equations and their generalizations, and applications of the equations and the solutions. Alexander D. Bruno and Alexander B. Batkhin, Russian Academy of Sciences, Moscow, Russia.
Anmerkung:
Description based upon print version of record
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Preface; I Plane Power Geometry; 1 Plane Power Geometry for One ODE and P1 - P6; 1.1 Statement of the Problem; 1.2 Computation of Truncated Equations; 1.3 Computation of Expansions of Solutions to the Initial Equation (1.1) .; 1.4 Extension of the Class of Solutions; 1.5 Solution of Truncated Equations; 1.6 Types of Expansions; 1.7 Painlevé Equations Pl; 2 New Simple Exact Solutions to Equation P6; 2.1 Introduction; 2.1.1 Power Geometry Essentials; 2.1.2 Matching "Heads" and "Tails" of Expansions; 2.2 Constructing the Template of an Exact Solution; 2.3 Results
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2.3.1 Known Exact Solutions to P62.3.2 Computed Solutions; 2.3.3 Generalization of Computed Solutions; 3 Convergence of a Formal Solution to an ODE; 3.1 The General Case; 3.2 The Case of Rational Power Exponents; 3.3 The Case of Complex Power Exponents; 3.4 On Solutions of the Sixth Painlevé Equation; 4 Asymptotic Expansions and Forms of Solutions to P6; 4.1 Asymptotic Expansions near Singular Points of the Equation; 4.2 Asymptotic Expansions near a Regular Point of the Equation; 4.3 Boutroux-Type Elliptic Asymptotic Forms; 5 Asymptotic Expansions of Solutions to P5; 5.1 Introduction
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5.2 Asymptotic Expansions of Solutions near Infinity5.3 Asymptotic Expansions of Solutions near Zero; 5.4 Asymptotic Expansions of Solutions in the Neighborhood of the Nonsingular Point of an Equation; II Space Power Geometry; 6 Space Power Geometry for one ODE and P1 - P4, P6; 6.1 Space Power Geometry; 6.2 Asymptotic Forms of Solutions to Painlevé Equations P1 - P4, P6; 6.2.1 Equation P1; 6.2.2 Equation P2; 6.2.3 Equation P3 for cd ≠ 0; 6.2.4 Equation P3 for c = 0 and ad ≠ 0; 6.2.5 Equation P3 for c = d = 0 and ab ≠ 0; 6.2.6 Equation P4; 6.2.7 Equation P6
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7 Elliptic and Periodic Asymptotic Forms of Solutions to P57.1 The Fifth Painlevé Equation; 7.2 The case δ ≠ 0; 7.2.1 General Properties of the P5 Equation; 7.2.2 The First Family of Elliptic Asymptotic Forms; 7.2.3 The First Family of Periodic Asymptotic Forms; 7.2.4 The Second Family of Periodic Asymptotic Forms; 7.3 The Case δ ≠ 0, γ ≠ 0; 7.3.1 General Properties; 7.3.2 The Second Family of Elliptic Asymptotic Forms; 7.3.3 The Third Family of Periodic Asymptotic Forms; 7.3.4 The Fourth Family of Periodic Asymptotic Forms; 7.4 The Results Obtained
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8 Regular Asymptotic Expansions of Solutions to One ODE and P1-P58.1 Introduction; 8.2 Finding Asymptotic Forms; 8.3 Computation of Expansions (8.2); 8.4 Equation P1; 8.5 Equation P2; 8.5.1 Elliptic Asymptotic Forms, Face Γ3(2); 8.5.2 Periodic Asymptotic Forms, Face Γ4(2); 8.6 Equation P3; 8.6.1 Case cd ≠ 0; 8.6.2 Case c = 0, ad ≠ 0; 8.6.3 Case c = d = 0, ab ≠ 0; 8.7 Equation P4; 8.7.1 Elliptic Asymptotic Forms, Face Γ3(2); 8.7.2 Periodic Asymptotic Forms, Face Γ4(2); 8.8 Equation P5; 8.8.1 Case d ≠ 0, Elliptic Asymptotic Forms, Face Γ1(2)
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8.8.2 Case d ≠ 0, Periodic Asymptotic Forms, Face Γ2(2)
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In English
Weitere Ausg.:
ISBN 9783110275582
Weitere Ausg.:
Erscheint auch als Druck-Ausgabe Painlevé equations and related topics Berlin [u.a.] : De Gruyter, 2012 ISBN 9783110275582
Weitere Ausg.:
ISBN 3110275589
Sprache:
Englisch
Schlagwort(e):
Painlevé-Gleichung
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Painlevé-Gleichung
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Konferenzschrift
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Konferenzschrift
DOI:
10.1515/9783110275667
URL:
Volltext
(lizenzpflichtig)
