Riemann-Hilbert problems, their numerical solution, and the computation of nonlinear special functions / Thomas Trogdon, New York University, New York, New York, Sheehan Olver, The University of Sydney, New South Wales, Australia.

Format:

Book

Author/Creator:

Trogdon, Thomas D., author.

Olver, Sheehan, author.

Contributor:

Society for Industrial and Applied Mathematics, publisher.

Series:

Other titles in applied mathematics.

Other titles in applied mathematics ; 146

Language:

English

Subjects (All):

Riemann-Hilbert problems.

Differentiable dynamical systems.

Physical Description:

1 PDF (xviii, 373 pages).

Place of Publication:

Philadelphia, Pennsylvania : Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104), [2015]

Language Note:

English

System Details:

Mode of access: World Wide Web.

System requirements: Adobe Acrobat Reader.

Summary:

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.

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.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references and index.

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

ISBN:

1-61197-420-8

OCLC:

930320797

Publisher Number:

OT146 SIAM