Riemann-Hilbert problems, their numerical solution, and the computation of nonlinear special functions (Q2798207)

The book continues investigations of \textit{A. S. Fokas} et al. [Painlevé transcendents. The Riemann-Hilbert approach. Providence, RI: AMS (2006; Zbl 1111.34001)], \textit{P. Deift} [Orthogonal polynomials and random matrices: a Riemann-Hilbert approach. Providence, RI: AMS (2000; Zbl 0997.47033)] and others, concerning applications of the Riemann-Hilbert (RH) boundary value problem.NEWLINENEWLINEThe main feature of this book is a lot of attention to numerical methods. In Part I the authors give a survey of applications where RH problems arise, and of the known techniques for solving them. Part II contains a detailed development of the numerical methods for approximation of the solutions of RH problems, and in Part III this methods are applied to specific integrable equations: the Korteveg-de Vries equation and its modifications, the nonlinear Schrödinger equations, the Painlevé II transcendents and some others.