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Author: Percy Deift
Publisher: American Mathematical Soc.
ISBN: 0821806912
Category : Mathematics
Languages : en
Pages : 233
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Book Description
In this book, the authors describe a continuum limit of the Toda ODE system, obtained by taking as initial data for the finite lattice successively finer discretizations of two smooth functions. Using the integrability of the finite Toda lattice, the authors adapt the method introduced by Lax and Levermore for the study of the small dispersion limit of the Korteweg de Vries equations to the case of the Toda lattice. A general class of initial data is considered which permits, in particular, the formation of shocks. A feature of the analysis in this book is an extensive use of techniques from the theory of Riemann-Hilbert problems.
Author: Percy Deift
Publisher: American Mathematical Soc.
ISBN: 0821806912
Category : Mathematics
Languages : en
Pages : 233
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Book Description
In this book, the authors describe a continuum limit of the Toda ODE system, obtained by taking as initial data for the finite lattice successively finer discretizations of two smooth functions. Using the integrability of the finite Toda lattice, the authors adapt the method introduced by Lax and Levermore for the study of the small dispersion limit of the Korteweg de Vries equations to the case of the Toda lattice. A general class of initial data is considered which permits, in particular, the formation of shocks. A feature of the analysis in this book is an extensive use of techniques from the theory of Riemann-Hilbert problems.
Author: Kenneth Dean T-R Mclaughlin
Publisher:
ISBN:
Category :
Languages : en
Pages : 250
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Book Description
Author: Percy Deift
Publisher: Oxford University Press, USA
ISBN: 9781470402136
Category : SCIENCE
Languages : en
Pages : 233
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Book Description
Content Description #"January 1998, volume 131, number 624 (end of volume)."#Includes bibliographical references.
Author: Percy Deift
Publisher: American Mathematical Soc.
ISBN: 9780821863473
Category : Mathematics
Languages : en
Pages : 236
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Book Description
In this book, the authors describe a continuum limit of the Toda ODE system, obtained by taking as initial data for the finite lattice successively finer discretizations of two smooth functions. A novel feature of the analysis in this book is an extensive use of techniques from the theory of Riemann-Hilbert problems.
Author: Roger W. Brockett
Publisher:
ISBN:
Category :
Languages : en
Pages : 14
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Book Description
Author: Fritz Gesztesy
Publisher: Cambridge University Press
ISBN: 1139473778
Category : Mathematics
Languages : en
Pages : 438
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Book Description
As a partner to Volume 1: Dimensional Continuous Models, this monograph provides a self-contained introduction to algebro-geometric solutions of completely integrable, nonlinear, partial differential-difference equations, also known as soliton equations. The systems studied in this volume include the Toda lattice hierarchy, the Kac-van Moerbeke hierarchy, and the Ablowitz-Ladik hierarchy. An extensive treatment of the class of algebro-geometric solutions in the stationary as well as time-dependent contexts is provided. The theory presented includes trace formulas, algebro-geometric initial value problems, Baker-Akhiezer functions, and theta function representations of all relevant quantities involved. The book uses basic techniques from the theory of difference equations and spectral analysis, some elements of algebraic geometry and especially, the theory of compact Riemann surfaces. The presentation is constructive and rigorous, with ample background material provided in various appendices. Detailed notes for each chapter, together with an exhaustive bibliography, enhance understanding of the main results.
Author: Decio Levi
Publisher: Springer
ISBN: 3319566660
Category : Science
Languages : en
Pages : 441
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Book Description
This book shows how Lie group and integrability techniques, originally developed for differential equations, have been adapted to the case of difference equations. Difference equations are playing an increasingly important role in the natural sciences. Indeed, many phenomena are inherently discrete and thus naturally described by difference equations. More fundamentally, in subatomic physics, space-time may actually be discrete. Differential equations would then just be approximations of more basic discrete ones. Moreover, when using differential equations to analyze continuous processes, it is often necessary to resort to numerical methods. This always involves a discretization of the differential equations involved, thus replacing them by difference ones. Each of the nine peer-reviewed chapters in this volume serves as a self-contained treatment of a topic, containing introductory material as well as the latest research results and exercises. Each chapter is presented by one or more early career researchers in the specific field of their expertise and, in turn, written for early career researchers. As a survey of the current state of the art, this book will serve as a valuable reference and is particularly well suited as an introduction to the field of symmetries and integrability of difference equations. Therefore, the book will be welcomed by advanced undergraduate and graduate students as well as by more advanced researchers.
Author: Peter D. Lax
Publisher: American Mathematical Soc.
ISBN: 0821806572
Category : Mathematics
Languages : en
Pages : 407
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Book Description
Lax and Nirenberg are two of the most distinguished mathematicians of our times. Their work on partial differential equations (PDEs) over the last half-century has dramatically advanced the subject and has profoundly influenced the course of mathematics. A huge part of the development in PDEs during this period has either been through their work, motivated by it or achieved by their postdocs and students. A large number of mathematicians honored these two exceptional scientists in a week-long conference in Venice (June 1996) on the occasion of their 70th birthdays. This volume contains the proceedings of the conference, which focused on the modern theory of nonlinear PDEs and their applications. Among the topics treated are turbulence, kinetic models of a rarefied gas, vortex filaments, dispersive waves, singular limits and blow-up solutions, conservation laws, Hamiltonian systems and others. The conference served as a forum for the dissemination of new scientific ideas and discoveries and enhanced scientific communication by bringing together such a large number of scientists working in related fields. THe event allowed the international mathematics community to honor two of its outstanding members.
Author: J. Baik
Publisher: Princeton University Press
ISBN: 1400837138
Category : Mathematics
Languages : en
Pages : 179
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Book Description
This book describes the theory and applications of discrete orthogonal polynomials--polynomials that are orthogonal on a finite set. Unlike other books, Discrete Orthogonal Polynomials addresses completely general weight functions and presents a new methodology for handling the discrete weights case. J. Baik, T. Kriecherbauer, K. T.-R. McLaughlin & P. D. Miller focus on asymptotic aspects of general, nonclassical discrete orthogonal polynomials and set out applications of current interest. Topics covered include the probability theory of discrete orthogonal polynomial ensembles and the continuum limit of the Toda lattice. The primary concern throughout is the asymptotic behavior of discrete orthogonal polynomials for general, nonclassical measures, in the joint limit where the degree increases as some fraction of the total number of points of collocation. The book formulates the orthogonality conditions defining these polynomials as a kind of Riemann-Hilbert problem and then generalizes the steepest descent method for such a problem to carry out the necessary asymptotic analysis.
Author: Percy Deift
Publisher: Cambridge University Press
ISBN: 1107079926
Category : Language Arts & Disciplines
Languages : en
Pages : 539
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Book Description
This volume includes review articles and research contributions on long-standing questions on universalities of Wigner matrices and beta-ensembles.
