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Author : Gunter Semmler
Publisher :
ISBN 13 :
Total Pages : 48 pages
Book Rating : 4.:/5 (313 download)
Download or read book Nonlinear Riemann-Hilbert Problems with Continuous Restriction Curves written by Gunter Semmler and published by . This book was released on 2000 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Elias Wegert
Publisher : Wiley-VCH
ISBN 13 :
Total Pages : 248 pages
Book Rating : 4.3/5 (91 download)
Download or read book Nonlinear Boundary Value Problems for Holomorphic Functions and Singular Integral Equations written by Elias Wegert and published by Wiley-VCH. This book was released on 1992-05-08 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covers various topics in nonlinear boundary value problems for holomorphic functions, including existence and uniqueness results, questions concerning parameter dependence, regularity theorems, several procedures for numerically solving such problems, and applications to nonlinear singular integral equations. The emphasis is mainly on geometric aspects. Numerical methods are discussed. This text requires only an elementary knowledge of function theory. Includes a 13-page bibliography. Distributed in the US by VCH. Annotation copyright by Book News, Inc., Portland, OR
Author : Thomas Trogdon
Publisher : SIAM
ISBN 13 : 1611974194
Total Pages : 370 pages
Book Rating : 4.6/5 (119 download)
Download or read book Riemann-Hilbert Problems, Their Numerical Solution, and the Computation of Nonlinear Special Functions written by Thomas Trogdon and published by SIAM. This book was released on 2015-12-22 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.?
Author : Athanassios S. Fokas
Publisher : American Mathematical Society
ISBN 13 : 1470475561
Total Pages : 570 pages
Book Rating : 4.4/5 (74 download)
Download or read book Painlevé Transcendents written by Athanassios S. Fokas and published by American Mathematical Society. This book was released on 2023-11-20 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt: At the turn of the twentieth century, the French mathematician Paul Painlevé and his students classified second order nonlinear ordinary differential equations with the property that the location of possible branch points and essential singularities of their solutions does not depend on initial conditions. It turned out that there are only six such equations (up to natural equivalence), which later became known as Painlevé I–VI. Although these equations were initially obtained answering a strictly mathematical question, they appeared later in an astonishing (and growing) range of applications, including, e.g., statistical physics, fluid mechanics, random matrices, and orthogonal polynomials. Actually, it is now becoming clear that the Painlevé transcendents (i.e., the solutions of the Painlevé equations) play the same role in nonlinear mathematical physics that the classical special functions, such as Airy and Bessel functions, play in linear physics. The explicit formulas relating the asymptotic behaviour of the classical special functions at different critical points play a crucial role in the applications of these functions. It is shown in this book that even though the six Painlevé equations are nonlinear, it is still possible, using a new technique called the Riemann-Hilbert formalism, to obtain analogous explicit formulas for the Painlevé transcendents. This striking fact, apparently unknown to Painlevé and his contemporaries, is the key ingredient for the remarkable applicability of these “nonlinear special functions”. The book describes in detail the Riemann-Hilbert method and emphasizes its close connection to classical monodromy theory of linear equations as well as to modern theory of integrable systems. In addition, the book contains an ample collection of material concerning the asymptotics of the Painlevé functions and their various applications, which makes it a good reference source for everyone working in the theory and applications of Painlevé equations and related areas.
Author : Spyridon Kamvissis
Publisher : Princeton University Press
ISBN 13 : 1400837189
Total Pages : 280 pages
Book Rating : 4.4/5 (8 download)
Download or read book Semiclassical Soliton Ensembles for the Focusing Nonlinear Schrödinger Equation (AM-154) written by Spyridon Kamvissis and published by Princeton University Press. This book was released on 2003-08-18 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 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. This problem is a key model in nonlinear optical physics and has increasingly important applications in the telecommunications industry. The authors exploit complete integrability to establish pointwise asymptotics for this problem's solution in the semiclassical regime and explicit integration for the underlying nonlinear, elliptic, partial differential equations suspected of governing the semiclassical behavior. In doing so they also aim to explain the observed gradient catastrophe for the underlying nonlinear elliptic partial differential equations, and to set forth a detailed, pointwise asymptotic description of the violent oscillations that emerge following the gradient catastrophe. To achieve this, the authors have extended the reach of two powerful analytical techniques that have arisen through the asymptotic analysis of integrable systems: the Lax-Levermore-Venakides variational approach to singular limits in integrable systems, and Deift and Zhou's nonlinear Steepest-Descent/Stationary Phase method for the analysis of Riemann-Hilbert problems. In particular, they introduce a systematic procedure for handling certain Riemann-Hilbert problems with poles accumulating on curves in the plane. This book, which includes an appendix on the use of the Fredholm theory for Riemann-Hilbert problems in the Hölder class, is intended for researchers and graduate students of applied mathematics and analysis, especially those with an interest in integrable systems, nonlinear waves, or complex analysis.
Author : Franc Forstnerič
Publisher :
ISBN 13 :
Total Pages : 26 pages
Book Rating : 4.:/5 (16 download)
Download or read book On the nonlinear Riemann Hilbert problem written by Franc Forstnerič and published by . This book was released on 1987 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Gunter Semmler
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (723 download)
Download or read book Nonlinear Riemann-Hilbert Problems written by Gunter Semmler and published by . This book was released on 2004 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : D. V. Anosov
Publisher : Springer Science & Business Media
ISBN 13 : 3322929094
Total Pages : 202 pages
Book Rating : 4.3/5 (229 download)
Download or read book The Riemann-Hilbert Problem written by D. V. Anosov and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Riemann-Hilbert problem (Hilbert's 21st problem) belongs to the theory of linear systems of ordinary differential equations in the complex domain. The problem concerns the existence of a Fuchsian system with prescribed singularities and monodromy. Hilbert was convinced that such a system always exists. However, this turned out to be a rare case of a wrong forecast made by him. In 1989 the second author (A. B.) discovered a counterexample, thus obtaining a negative solution to Hilbert's 21st problem in its original form.
Author : Thomas Trogdon
Publisher : SIAM
ISBN 13 : 1611974208
Total Pages : 370 pages
Book Rating : 4.6/5 (119 download)
Download or read book Riemann-Hilbert Problems, Their Numerical Solution, and the Computation of Nonlinear Special Functions written by Thomas Trogdon and published by SIAM. This book was released on 2015-12-22 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Thomas D. Trogdon
Publisher :
ISBN 13 :
Total Pages : 318 pages
Book Rating : 4.:/5 (881 download)
Download or read book Riemann-Hilbert Problems, Their Numerical Solution and the Computation of Nonlinear Special Functions written by Thomas D. Trogdon and published by . This book was released on 2013 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: The computation of special functions has important implications throughout engineering and the physical sciences. Nonlinear special functions include the solutions of integrable partial differential equations and the Painleve transcendents. Many problems in water wave theory, nonlinear optics and statistical mechanics are reduced to the study of a nonlinear special function in particular limits. The universal object that these functions share is a Riemann-Hilbert representation: the nonlinear special function can be recovered from the solution of a Riemann-Hilbert problem (RHP). A RHP consists of finding a piecewise-analytic function in the complex plane when the behavior of its discontinuities is specified. In this dissertation, the applied theory of Riemann-Hilbert problems, using both Holder and Lebesgue spaces, is reviewed. The numerical solution of RHPs is discussed. Furthermore, the uniform approximation theory for the numerical solution of RHPs is presented, proving that in certain cases the convergence of the numerical method is uniform with respect to a parameter. This theory shares close relation to the method of nonlinear steepest descent for RHPs. The inverse scattering transform for the Korteweg-de Vries and Nonlinear Schroedinger equation is made effective by solving the associated RHPs numerically. This technique is extended to solve the Painleve II equation numerically. Similar Riemann-Hilbert techniques are used to compute the so-called finite-genus solutions of the Korteweg-de Vries equation. This involves ideas from Riemann surface theory. Finally, the methodology is applied to compute orthogonal polynomials with exponential weights. This allows for the computation of statistical quantities stemming from random matrix ensembles.
Author : B L J Braaksma
Publisher : World Scientific
ISBN 13 : 9814548081
Total Pages : 342 pages
Book Rating : 4.8/5 (145 download)
Download or read book The Stokes Phenomenon And Hilbert's 16th Problem written by B L J Braaksma and published by World Scientific. This book was released on 1996-05-06 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 16th Problem of Hilbert is one of the most famous remaining unsolved problems of mathematics. It concerns whether a polynomial vector field on the plane has a finite number of limit cycles. There is a strong connection with divergent solutions of differential equations, where a central role is played by the Stokes Phenomenon, the change in asymptotic behaviour of the solutions in different sectors of the complex plane.The contributions to these proceedings survey both of these themes, including historical and modern theoretical points of view. Topics covered include the Riemann-Hilbert problem, Painleve equations, nonlinear Stokes phenomena, and the inverse Galois problem.
Author : Elias Wegert
Publisher :
ISBN 13 :
Total Pages : 109 pages
Book Rating : 4.:/5 (312 download)
Download or read book On the Numerical Solution of Nonlinear Riemann Hilbert Problems written by Elias Wegert and published by . This book was released on 1996 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Michail A. Efendiev
Publisher :
ISBN 13 :
Total Pages : 21 pages
Book Rating : 4.:/5 (18 download)
Download or read book On Nonlinear Riemann-Hilbert Problems with Discontinuous Coefficients written by Michail A. Efendiev and published by . This book was released on 2006 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (227 download)
Download or read book The Solution of a Certain Nonlinear Riemann-Hilbert Problem with an Application written by and published by . This book was released on 1971 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The report shows that the nonlinear barrier equation F(+)(zeta)F( - )(zeta) + mu(zeta)(F(+)(zeta) + F( - )(zeta)) + sigma(zeta) = 0 can be solved in closed form provided mu(zeta), sigma(zeta) are Holder continuous and so related that signa(zeta) + S squared(zeta) + 2S(zeta)mu(zeta) = ((zeta)-alpha)(zeta-beta)) sup Kappa t squared(zeta) where s(zeta) and t(zeta) are rational functions and kappa = 0, or 1. (Author).
Author : Lothar von Wolfersdorf
Publisher :
ISBN 13 :
Total Pages : 32 pages
Book Rating : 4.:/5 (258 download)
Download or read book A Class of Nonlinear Riemann-Hilbert Problems for Holomorphic Functions written by Lothar von Wolfersdorf and published by . This book was released on 1982 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Aspects of Mathematics written by and published by . This book was released on 1981 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : D. V. Anosov
Publisher :
ISBN 13 :
Total Pages : 190 pages
Book Rating : 4.:/5 (11 download)
Download or read book The Riemann-Hilbert Problem written by D. V. Anosov and published by . This book was released on 1994 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt:
