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Format: 1 online resource (286p.)

ISBN: 9783110275667

Series Statement: De Gruyter Proceedings in Mathematics

Content: 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 Steklov Institute of Mathematics of the Russian Academy of Sciences, in Saint Petersburg on June 17 to 23, 2011. The survey articles discuss the following topics: General ordinary differential equations Painlevé equations and their generalizations Painlevé property Discrete Painlevé equations Properties of solutions of all mentioned above equations:– Asymptotic forms and asymptotic expansions– Connections of asymptotic forms of a solution near different points– Convergency and asymptotic character of a formal solution– New types of asymptotic forms and asymptotic expansions– Riemann-Hilbert problems– Isomonodromic deformations of linear systems– Symmetries and transformations of solutions– Algebraic solutions Reductions of PDE to Painlevé equations and their generalizations Ordinary Differential Equations systems equivalent to Painlevé equations and their generalizations Applications of the equations and the solutions

Note: Frontmatter -- , Preface -- , Contents -- , Part I. Plane Power Geometry -- , Chapter 1. Plane Power Geometry for One ODE and P1–P6 -- , Chapter 2. New Simple Exact Solutions to Equation P6 -- , Chapter 3. Convergence of a Formal Solution to an ODE -- , Chapter 4. Asymptotic Expansions and Forms of Solutions to P6 -- , Chapter 5. Asymptotic Expansions of Solutions to P5 -- , Part II. Space Power Geometry -- , Chapter 6. Space Power Geometry for one ODE and P1–P4, P6 -- , Chapter 7. Elliptic and Periodic Asymptotic Forms of Solutions to P5 -- , Chapter 8. Regular Asymptotic Expansions of Solutions to One ODE and P1–P5 -- , Part III. Isomondromy Deformations -- , Chapter 9. Isomonodromic Deformations on Riemann Surfaces -- , Chapter 10. On Birational Darboux Coordinates of Isomonodromic Deformation Equations Phase Space -- , Chapter 11. On the Malgrange Isomonodromic Deformations of Nonresonant Irregular Systems -- , Chapter 12. Critical behavior of P6 Functions from the Isomonodromy Deformations Approach -- , Chapter 13. Isomonodromy Deformation of the Heun Class Equation -- , Chapter 14. Isomonodromy Deformations and Hypergeometric-Type Systems -- , Chapter 15. A Monodromy Problem Connected with P6 -- , Chapter 16. Monodromy Evolving Deformations and Confluent Halphen’s Systems -- , Chapter 17. On the Gauge Transformation of the Sixth Painlevé Equation -- , Chapter 18. Expansions for Solutions of the Schlesinger Equation at a Singular Point -- , Part IV. Painlevé Property -- , Chapter 19. Painleve Analysis of Lotka–Volterra Equations -- , Chapter 20. Painlevé Test and Briot–Bouquet Systems -- , Chapter 21. Solutions of the Chazy System -- , Chapter 22. Third-Order Ordinary Differential Equations with the Painlevé Test -- , Chapter 23. Analytic Properties of Solutions of a Class of Third-Order Equations with an Irrational Right-Hand Side -- , Part V. Other Aspects -- , Chapter 24. The Sixth Painlevé Transcendent and Uniformizable Orbifolds -- , Chapter 25. On Uniformizable Representation for Abelian Integrals -- , Chapter 26. Phase Shift for a Special Solution to the Korteweg–de Vries Equation in the Whitham Zone -- , Chapter 27. Fuchsian Reduction of Differential Equations -- , Chapter 28. The Voros Coefficient and the Parametric Stokes Phenomenon for the Second Painlevé Equation -- , Chapter 29. Integral Symmetry and the Deformed Hypergeometric Equation -- , Chapter 30. Integral Symmetries for Confluent Heun Equations and Symmetries of Painlevé Equation P5 -- , Chapter 31. From the Tau Function of Painlevé P6 Equation to Moduli Spaces -- , Chapter 32. On particular Solutions of q-Painlevé Equations and q-Hypergeometric Equations -- , Chapter 33. Derivation of Painlevé Equations by Antiquantization -- , Chapter 34. Integral Transformation of Heun’s Equation and Apparent Singularity -- , Chapter 35. Painlevé Analysis of Solutions to Some Nonlinear Differential Equations and their Systems Associated with Models of the Random-Matrix Type -- , Chapter 36. Reductions on the Lattice and Painlevé Equations P2, P5, P6 -- , Comments , In English.

Additional Edition: ISBN 978-3-11-027558-2

Language: English

DOI: 10.1515/9783110275667

URL: https://doi.org/10.1515/9783110275667

URL: https://doi.org/10.1515/9783110275667

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Format: xiv, 272 p. : , ill.

Edition: Electronic reproduction. Ann Arbor, MI : ProQuest, 2015. Available via World Wide Web. Access may be limited to ProQuest affiliated libraries.

Series Statement: De Gruyter proceedings in mathematics

Language: English

Keywords: Electronic books.

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Format: 1 Online-Ressource (XIV, 274 Seiten) , Diagramme

ISBN: 9783110275667 , 1283628414 , 9781283628419

Series Statement: De Gruyter Proceedings in Mathematics

Content: 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.

Note: Description based upon print version of record , 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 , 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 , 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 , 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 , 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) , 8.8.2 Case d ≠ 0, Periodic Asymptotic Forms, Face Γ2(2) , In English

Additional Edition: ISBN 9783110275582

Additional Edition: Erscheint auch als Druck-Ausgabe Painlevé equations and related topics Berlin [u.a.] : De Gruyter, 2012 ISBN 9783110275582

Additional Edition: ISBN 3110275589

Language: English

Keywords: Painlevé-Gleichung ; Painlevé-Gleichung ; Konferenzschrift ; Konferenzschrift

DOI: 10.1515/9783110275667

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Format: 1 online resource (272 p.)

ISBN: 9783110275667 , 9783110238570

Series Statement: De Gruyter Proceedings in Mathematics

Content: 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 Steklov Institute of Mathematics of the Russian Academy of Sciences, in Saint Petersburg on June 17 to 23, 2011. The survey articles discuss the following topics: General ordinary differential equations Painlevé equations and their generalizations Painlevé property Discrete Painlevé equations Properties of solutions of all mentioned above equations:- Asymptotic forms and asymptotic expansions- Connections of asymptotic forms of a solution near different points- Convergency and asymptotic character of a formal solution- New types of asymptotic forms and asymptotic expansions- Riemann-Hilbert problems- Isomonodromic deformations of linear systems- Symmetries and transformations of solutions- Algebraic solutions Reductions of PDE to Painlevé equations and their generalizations Ordinary Differential Equations systems equivalent to Painlevé equations and their generalizations Applications of the equations and the solutions

Note: Frontmatter -- , Preface -- , Contents -- , Part I. Plane Power Geometry -- , Chapter 1. Plane Power Geometry for One ODE and P1-P6 -- , Chapter 2. New Simple Exact Solutions to Equation P6 -- , Chapter 3. Convergence of a Formal Solution to an ODE -- , Chapter 4. Asymptotic Expansions and Forms of Solutions to P6 -- , Chapter 5. Asymptotic Expansions of Solutions to P5 -- , Part II. Space Power Geometry -- , Chapter 6. Space Power Geometry for one ODE and P1-P4, P6 -- , Chapter 7. Elliptic and Periodic Asymptotic Forms of Solutions to P5 -- , Chapter 8. Regular Asymptotic Expansions of Solutions to One ODE and P1-P5 -- , Part III. Isomondromy Deformations -- , Chapter 9. Isomonodromic Deformations on Riemann Surfaces -- , Chapter 10. On Birational Darboux Coordinates of Isomonodromic Deformation Equations Phase Space -- , Chapter 11. On the Malgrange Isomonodromic Deformations of Nonresonant Irregular Systems -- , Chapter 12. Critical behavior of P6 Functions from the Isomonodromy Deformations Approach -- , Chapter 13. Isomonodromy Deformation of the Heun Class Equation -- , Chapter 14. Isomonodromy Deformations and Hypergeometric-Type Systems -- , Chapter 15. A Monodromy Problem Connected with P6 -- , Chapter 16. Monodromy Evolving Deformations and Confluent Halphen's Systems -- , Chapter 17. On the Gauge Transformation of the Sixth Painlevé Equation -- , Chapter 18. Expansions for Solutions of the Schlesinger Equation at a Singular Point -- , Part IV. Painlevé Property -- , Chapter 19. Painleve Analysis of Lotka-Volterra Equations -- , Chapter 20. Painlevé Test and Briot-Bouquet Systems -- , Chapter 21. Solutions of the Chazy System -- , Chapter 22. Third-Order Ordinary Differential Equations with the Painlevé Test -- , Chapter 23. Analytic Properties of Solutions of a Class of Third-Order Equations with an Irrational Right-Hand Side -- , Part V. Other Aspects -- , Chapter 24. The Sixth Painlevé Transcendent and Uniformizable Orbifolds -- , Chapter 25. On Uniformizable Representation for Abelian Integrals -- , Chapter 26. Phase Shift for a Special Solution to the Korteweg-de Vries Equation in the Whitham Zone -- , Chapter 27. Fuchsian Reduction of Differential Equations -- , Chapter 28. The Voros Coefficient and the Parametric Stokes Phenomenon for the Second Painlevé Equation -- , Chapter 29. Integral Symmetry and the Deformed Hypergeometric Equation -- , Chapter 30. Integral Symmetries for Confluent Heun Equations and Symmetries of Painlevé Equation P5 -- , Chapter 31. From the Tau Function of Painlevé P6 Equation to Moduli Spaces -- , Chapter 32. On particular Solutions of q-Painlevé Equations and q-Hypergeometric Equations -- , Chapter 33. Derivation of Painlevé Equations by Antiquantization -- , Chapter 34. Integral Transformation of Heun's Equation and Apparent Singularity -- , Chapter 35. Painlevé Analysis of Solutions to Some Nonlinear Differential Equations and their Systems Associated with Models of the Random-Matrix Type -- , Chapter 36. Reductions on the Lattice and Painlevé Equations P2, P5, P6 -- , Comments , Mode of access: Internet via World Wide Web. , In English.

In: DGBA Backlist Complete English Language 2000-2014 PART1, De Gruyter, 9783110238570

In: DGBA Backlist Mathematics 2000-2014 (EN), De Gruyter, 9783110238471

In: DGBA Mathematics - 2000 - 2014, De Gruyter, 9783110637205

In: E-BOOK GESAMTPAKET / COMPLETE PACKAGE 2012, De Gruyter, 9783110288995

In: E-BOOK PACKAGE MATHEMATICS, PHYSICS, ENGINEERING 2012, De Gruyter, 9783110293722

In: E-BOOK PAKET MATHEMATIK, PHYSIK, INGENIEURWISS. 2012, De Gruyter, 9783110288926

Additional Edition: ISBN 9783110275582

Language: English

DOI: 10.1515/9783110275667

URL: https://doi.org/10.1515/9783110275667

URL: https://www.degruyter.com/isbn/9783110275667

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