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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
Get Book Here
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: Anton Dzhamay
Publisher: American Mathematical Soc.
ISBN: 0821887475
Category : Mathematics
Languages : en
Pages : 363
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Book Description
This volume contains the proceedings of the AMS Special Session on Algebraic and Geometric Aspects of Integrable Systems and Random Matrices, held from January 6-7, 2012, in Boston, MA. The very wide range of topics represented in this volume illustrates
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: Michel Remoissenet
Publisher: Springer Science & Business Media
ISBN: 3662030578
Category : Science
Languages : en
Pages : 248
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Book Description
Nonlinearity is a fascinating element of nature whose importance has been appreciated for many years when considering large-amplitude wave motions observed in various fields ranging from fluids and plasmas to solid-state, chemical, biological, and geological systems. Localized large-amplitude waves called solitons, which propagate without spreading and have particle-like properties, represent one of the most striking aspects of nonlinear phenomena. Although a wealth of literature on the subject, including theoretical and numerical studies, is available in good recent books and research journals, very little material has found its way into introductory texbooks and curricula. This is perhaps due to a belief that nonlinear physics is difficult and cannot be taught at an introductory level to undergraduate students and practitioners. Consequently, there is considerable interest in developing practical material suitable for students, at the lowest introductory level. This book is intended to be an elementary introduction to the physics of solitons, for students, physicists, engineers and practitioners. We present the modeling of nonlinear phenomena where soliton-like waves are involved, together with applications to a wide variety of concrete systems and experiments. This book is designed as a book of physical ideas and basic methods and not as an up-to-the minute book concerned with the latest research results. The background in physics and the amount of mathematical knowledge assumed of the reader is within that usually accumulated by junior or senior students in physics.
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: Helge Holden
Publisher: Springer Science & Business Media
ISBN: 3642013732
Category : Mathematics
Languages : en
Pages : 325
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Book Description
The book presents the winners of the first five Abel Prizes in mathematics: 2003 Jean-Pierre Serre; 2004 Sir Michael Atiyah and Isadore Singer; 2005 Peter D. Lax; 2006 Lennart Carleson; and 2007 S.R. Srinivasa Varadhan. Each laureate provides an autobiography or an interview, a curriculum vitae, and a complete bibliography. This is complemented by a scholarly description of their work written by leading experts in the field and by a brief history of the Abel Prize. Interviews with the laureates can be found at http://extras.springer.com .
Author: Spyridon Kamvissis
Publisher: Princeton University Press
ISBN: 069111482X
Category : Mathematics
Languages : en
Pages : 281
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Book Description
Providing an asymptotic analysis via completely integrable techniques, of the initial value problem for the focusing nonlinear Schrodinger equation in the semiclassical asymptotic regime, this text exploits complete integrability to establish pointwise asymptotics for this problem's solution.
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.
