Discrete Systems and Integrability

Discrete Systems and Integrability
Title Discrete Systems and Integrability PDF eBook
Author J. Hietarinta
Publisher Cambridge University Press
Pages 461
Release 2016-09
Genre Mathematics
ISBN 1107042720

Download Discrete Systems and Integrability Book in PDF, Epub and Kindle

A first introduction to the theory of discrete integrable systems at a level suitable for students and non-experts.

The Problem of Integrable Discretization

The Problem of Integrable Discretization
Title The Problem of Integrable Discretization PDF eBook
Author Yuri B. Suris
Publisher Birkhäuser
Pages 1078
Release 2012-12-06
Genre Mathematics
ISBN 3034880162

Download The Problem of Integrable Discretization Book in PDF, Epub and Kindle

An exploration of the theory of discrete integrable systems, with an emphasis on the following general problem: how to discretize one or several of independent variables in a given integrable system of differential equations, maintaining the integrability property? This question (related in spirit to such a modern branch of numerical analysis as geometric integration) is treated in the book as an immanent part of the theory of integrable systems, also commonly termed as the theory of solitons. Most of the results are only available from recent journal publications, many of them are new. Thus, the book is a kind of encyclopedia on discrete integrable systems. It unifies the features of a research monograph and a handbook. It is supplied with an extensive bibliography and detailed bibliographic remarks at the end of each chapter. Largely self-contained, it will be accessible to graduate and post-graduate students as well as to researchers in the area of integrable dynamical systems.

Discrete Differential Geometry

Discrete Differential Geometry
Title Discrete Differential Geometry PDF eBook
Author Alexander I. Bobenko
Publisher American Mathematical Society
Pages 432
Release 2023-09-14
Genre Mathematics
ISBN 1470474565

Download Discrete Differential Geometry Book in PDF, Epub and Kindle

An emerging field of discrete differential geometry aims at the development of discrete equivalents of notions and methods of classical differential geometry. The latter appears as a limit of a refinement of the discretization. Current interest in discrete differential geometry derives not only from its importance in pure mathematics but also from its applications in computer graphics, theoretical physics, architecture, and numerics. Rather unexpectedly, the very basic structures of discrete differential geometry turn out to be related to the theory of integrable systems. One of the main goals of this book is to reveal this integrable structure of discrete differential geometry. For a given smooth geometry one can suggest many different discretizations. Which one is the best? This book answers this question by providing fundamental discretization principles and applying them to numerous concrete problems. It turns out that intelligent theoretical discretizations are distinguished also by their good performance in applications. The intended audience of this book is threefold. It is a textbook on discrete differential geometry and integrable systems suitable for a one semester graduate course. On the other hand, it is addressed to specialists in geometry and mathematical physics. It reflects the recent progress in discrete differential geometry and contains many original results. The third group of readers at which this book is targeted is formed by specialists in geometry processing, computer graphics, architectural design, numerical simulations, and animation. They may find here answers to the question “How do we discretize differential geometry?” arising in their specific field. Prerequisites for reading this book include standard undergraduate background (calculus and linear algebra). No knowledge of differential geometry is expected, although some familiarity with curves and surfaces can be helpful.

Integrable Systems

Integrable Systems
Title Integrable Systems PDF eBook
Author N.J. Hitchin
Publisher Oxford University Press, USA
Pages 148
Release 2013-03-14
Genre Mathematics
ISBN 0199676771

Download Integrable Systems Book in PDF, Epub and Kindle

Designed to give graduate students an understanding of integrable systems via the study of Riemann surfaces, loop groups, and twistors, this book has its origins in a lecture series given by the internationally renowned authors. Written in an accessible, informal style, it fills a gap in the existing literature.

Discrete Integrable Systems

Discrete Integrable Systems
Title Discrete Integrable Systems PDF eBook
Author Basil Grammaticos
Publisher
Pages 460
Release 2014-01-15
Genre
ISBN 9783662144602

Download Discrete Integrable Systems Book in PDF, Epub and Kindle

Symmetries, Integrable Systems and Representations

Symmetries, Integrable Systems and Representations
Title Symmetries, Integrable Systems and Representations PDF eBook
Author Kenji Iohara
Publisher Springer Science & Business Media
Pages 633
Release 2012-12-06
Genre Mathematics
ISBN 1447148630

Download Symmetries, Integrable Systems and Representations Book in PDF, Epub and Kindle

This volume is the result of two international workshops; Infinite Analysis 11 – Frontier of Integrability – held at University of Tokyo, Japan in July 25th to 29th, 2011, and Symmetries, Integrable Systems and Representations held at Université Claude Bernard Lyon 1, France in December 13th to 16th, 2011. Included are research articles based on the talks presented at the workshops, latest results obtained thereafter, and some review articles. The subjects discussed range across diverse areas such as algebraic geometry, combinatorics, differential equations, integrable systems, representation theory, solvable lattice models and special functions. Through these topics, the reader will find some recent developments in the field of mathematical physics and their interactions with several other domains.

Darboux Transformations in Integrable Systems

Darboux Transformations in Integrable Systems
Title Darboux Transformations in Integrable Systems PDF eBook
Author Chaohao Gu
Publisher Springer Science & Business Media
Pages 317
Release 2006-07-09
Genre Science
ISBN 1402030886

Download Darboux Transformations in Integrable Systems Book in PDF, Epub and Kindle

The Darboux transformation approach is one of the most effective methods for constructing explicit solutions of partial differential equations which are called integrable systems and play important roles in mechanics, physics and differential geometry. This book presents the Darboux transformations in matrix form and provides purely algebraic algorithms for constructing the explicit solutions. A basis for using symbolic computations to obtain the explicit exact solutions for many integrable systems is established. Moreover, the behavior of simple and multi-solutions, even in multi-dimensional cases, can be elucidated clearly. The method covers a series of important equations such as various kinds of AKNS systems in R1+n, harmonic maps from 2-dimensional manifolds, self-dual Yang-Mills fields and the generalizations to higher dimensional case, theory of line congruences in three dimensions or higher dimensional space etc. All these cases are explained in detail. This book contains many results that were obtained by the authors in the past few years. Audience: The book has been written for specialists, teachers and graduate students (or undergraduate students of higher grade) in mathematics and physics.