Riemann-Hilbert Problems, Their Numerical Solution, and the Computation of Nonlinear Special Functions
- ISBN-10
- 1611974194
- ISBN-13
- 9781611974195
- Category
- Mathematics
- Pages
- 373
- Language
- English
- Published
- 2015-12-22
- Publisher
- SIAM
- Authors
- Thomas Trogdon, Sheehan Olver
Description
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, and a discussion of applications to integrable systems, differential equations, and special function theory. It also includes six fundamental examples and five more sophisticated examples of the analytical and numerical Riemann?Hilbert method, each of mathematical or physical significance or both.÷
Get the book
Other editions
-
- 2015-12-22
- 373 pages
- Ebook
- SIAM
Similar books
-
Unified Transform for Boundary Value Problems: Applications and Advances
By Athanasios S. Fokas, Beatrice Pelloni[20] S. Olver and T. Trogdon, Nonlinear steepest descent and numerical solution of RiemannHilbert problems, Comm. ... Riemann-Hilbert Problems, Their Numerical Solution and the Computation of Nonlinear Special Functions, PhD thesis, ...
-
Nonlinear Systems and Their Remarkable Mathematical Structures: Volume 3, Contributions from China
By Norbert Euler, Da-jun Zhang[30] Trogdon T and Olver S, Riemann-Hilbert problems, their numerical solution, and the computation of nonlinear special functions, SIAM, Philadelphia, PA, 2016. [31] Tzoar N and Jain M, Self-phase modulation in long-geometry optical ...
-
Nonlinear Dispersive Partial Differential Equations and Inverse Scattering
By Peter A. Perry, Catherine Sulem, Peter D. MillerThomas Trogdon and Sheehan Olver, Riemann-Hilbert problems, their numerical solution, and the computation of nonlinear special functions, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2016. MR 3450072 44.
-
Orthogonal Polynomials: Current Trends and Applications: Proceedings of the 7th EIBPOA Conference
By Francisco Marcellàn, Edmundo J. HuertasTrogdon, T., Olver, S.: Riemann-Hilbert Problems, Their Numerical Solution, and the Computation of Nonlinear Special Functions. Society for Industrial and Applied Mathematics (SIAM), Philadelphia (2016) 55. Van Assche, W.: Discrete ...
-
Symmetries and Integrability of Difference Equations: Lecture Notes of the Abecederian School of SIDE 12, Montreal 2016
By Pavel Winternitz, Decio Levi, Raphaël RebeloS. Olver, Numerical solution of Riemann–Hilbert problems: Painlevé II. ... 469(2149), 20120330 (2013) T. Trogdon, S. Olver, Riemann–Hilbert Problems, Their Numerical Solution and the Computation of Nonlinear Special Functions (SIAM, ...
-
Partial Differential Equations: An Introduction
By Walter A. StraussPartial Differential Equations presents a balanced and comprehensive introduction to the concepts and techniques required to solve problems containing unknown functions of multiple variables.
-
Semiclassical Soliton Ensembles for the Focusing Nonlinear Schrödinger Equation (AM-154)
By Peter D. Miller, Spyridon Kamvissis, Kenneth D.T-R McLaughlinThis book represents the first asymptotic analysis, via completely integrable techniques, of the initial value problem for the focusing nonlinear Schrödinger equation in the semiclassical asymptotic regime.
-
The Riemann-Hilbert Problem: A Publication from the Steklov Institute of Mathematics Adviser: Armen Sergeev
By D. V. Anosov, A. A. BolibruchThe Riemann-Hilbert problem (Hilbert's 21st problem) belongs to the theory of linear systems of ordinary differential equations in the complex domain.
-
Nonlinear Waves in Integrable and Non-integrable Systems
By Jianke YangThis book is intended for researchers and graduate students working in applied mathematics and various physical subjects where nonlinear wave phenomena arise (such as nonlinear optics, Bose-Einstein condensates, and fluid dynamics).
-
Nonlinear Waves in Integrable and Nonintegrable Systems
By Jianke YangPresents cutting-edge developments in the theory and experiments of nonlinear waves. Its comprehensive coverage of analytical and numerical methods for nonintegrable systems is the first of its kind.