Details

Subject(s)

• Riemann-Hilbert problems [Browse]
• Differentiable dynamical systems [Browse]

Publisher

• Society for Industrial and Applied Mathematics [Browse]

Author

• Olver, Sheehan [Browse]

Series

• Other titles in applied mathematics. [More in this series]
• Other titles in applied mathematics ; 146 [More in this series]

Summary note

Riemann-Hilbert problems are fundamental objects of study within complex analysis. Many problems in differential equations and integrable systems, probability and random matrix theory, and asymptotic analysis can be solved by reformulation as a Riemann-Hilbert problem. This book, the most comprehensive one to date on the applied and computational theory of Riemann-Hilbert problems, includes an introduction to computational complex analysis, an introduction to the applied theory of Riemann-Hilbert problems from an analytical and numerical perspective, a discussion of applications to integrable systems, differential equations, and special function theory, and six fundamental examples and five more sophisticated examples of the analytical and numerical Riemann-Hilbert method, each of mathematical or physical significance or both.

Notes

Bibliographic Level Mode of Issuance: Monograph

Bibliographic references

Includes bibliographical references and index.

System details

• Mode of access: World Wide Web.
• System requirements: Adobe Acrobat Reader.

Source of description

Title from title screen, viewed 11/19/2015.

Language note

English

Contents

• Preface
• Notation and abbreviations
• part I. Riemann-Hilbert problems
• 1. Classical applications of Riemann-Hilbert problems
• 2. Riemann-Hilbert problems
• 3. Inverse scattering and nonlinear steepest descent
• part II. Numerical solution of Riemann-Hilbert problems
• 4. Approximating functions
• 5. Numerical computation of Cauchy transforms
• 6. The numerical solution of Riemann-Hilbert problems
• 7. Uniform approximation theory for Riemann-Hilbert problems
• part III. The computation of nonlinear special functions and solutions of nonlinear PDEs
• 8. The Korteweg-de Vries and modified Korteweg-de Vries equations
• 9. The focusing and defocusing nonlinear Schrödinger equations
• 10. The Painlevé II transcendents
• 11. The finite-genus solutions of the Korteweg-de Vries equation
• 12. The dressing method and nonlinear superposition
• part IV. Appendices
• Appendix A. Function spaces and functional analysis
• Appendix B. Fourier and Chebyshev series
• Appendix C. Complex analysis
• Appendix D. Rational approximation
• Appendix E. Additional KDV results.

Show 20 more Contents items

ISBN

1-61197-420-8

Publisher no.

OT146

OCLC

930320797

Doi

• 10.1137/1.9781611974201

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