The Problem of Integrable Discretization
Title | The Problem of Integrable Discretization PDF eBook |
Author | Yuri B. Suris |
Publisher | Birkhäuser |
Total Pages | 1078 |
Release | 2012-12-06 |
Genre | Mathematics |
ISBN | 3034880162 |
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 Integrable Geometry and Physics
Title | Discrete Integrable Geometry and Physics PDF eBook |
Author | Alexander I. Bobenko |
Publisher | Clarendon Press |
Total Pages | 466 |
Release | 1999 |
Genre | Mathematics |
ISBN | 9780198501602 |
Recent interactions between the fields of geometry, classical and quantum dynamical systems, and visualization of geometric objects such as curves and surfaces have led to the observation that most concepts of surface theory and of the theory of integrable systems have natural discreteanalogues. These are characterized by the property that the corresponding difference equations are integrable, and has led in turn to some important applications in areas of condensed matter physics and quantum field theory, amongst others. The book combines the efforts of a distinguished team ofauthors from various fields in mathematics and physics in an effort to provide an overview of the subject. The mathematical concepts of discrete geometry and discrete integrable systems are firstly presented as fundamental and valuable theories in themselves. In the following part these concepts areput into the context of classical and quantum dynamics.
Discrete Systems and Integrability
Title | Discrete Systems and Integrability PDF eBook |
Author | J. Hietarinta |
Publisher | Cambridge University Press |
Total Pages | 461 |
Release | 2016-09 |
Genre | Mathematics |
ISBN | 1107042720 |
A first introduction to the theory of discrete integrable systems at a level suitable for students and non-experts.
Symmetries and Integrability of Difference Equations
Title | Symmetries and Integrability of Difference Equations PDF eBook |
Author | Peter A. Clarkson |
Publisher | Cambridge University Press |
Total Pages | 444 |
Release | 1999-02-04 |
Genre | Mathematics |
ISBN | 9780521596992 |
This volume comprises state-of-the-art articles in discrete integrable systems.
Discrete and Continuous Nonlinear Schrödinger Systems
Title | Discrete and Continuous Nonlinear Schrödinger Systems PDF eBook |
Author | M. J. Ablowitz |
Publisher | Cambridge University Press |
Total Pages | 276 |
Release | 2004 |
Genre | Mathematics |
ISBN | 9780521534376 |
This book presents a detailed mathematical analysis of scattering theory, obtains soliton solutions, and analyzes soliton interactions, both scalar and vector.
Integrable Hamiltonian Hierarchies
Title | Integrable Hamiltonian Hierarchies PDF eBook |
Author | Vladimir Gerdjikov |
Publisher | Springer |
Total Pages | 645 |
Release | 2008-12-02 |
Genre | Science |
ISBN | 3540770542 |
This book presents a detailed derivation of the spectral properties of the Recursion Operators allowing one to derive all the fundamental properties of the soliton equations and to study their hierarchies.
Continuous Symmetries and Integrability of Discrete Equations
Title | Continuous Symmetries and Integrability of Discrete Equations PDF eBook |
Author | Decio Levi |
Publisher | American Mathematical Society, Centre de Recherches Mathématiques |
Total Pages | 520 |
Release | 2023-01-23 |
Genre | Mathematics |
ISBN | 0821843540 |
This book on integrable systems and symmetries presents new results on applications of symmetries and integrability techniques to the case of equations defined on the lattice. This relatively new field has many applications, for example, in describing the evolution of crystals and molecular systems defined on lattices, and in finding numerical approximations for differential equations preserving their symmetries. The book contains three chapters and five appendices. The first chapter is an introduction to the general ideas about symmetries, lattices, differential difference and partial difference equations and Lie point symmetries defined on them. Chapter 2 deals with integrable and linearizable systems in two dimensions. The authors start from the prototype of integrable and linearizable partial differential equations, the Korteweg de Vries and the Burgers equations. Then they consider the best known integrable differential difference and partial difference equations. Chapter 3 considers generalized symmetries and conserved densities as integrability criteria. The appendices provide details which may help the readers' understanding of the subjects presented in Chapters 2 and 3. This book is written for PhD students and early researchers, both in theoretical physics and in applied mathematics, who are interested in the study of symmetries and integrability of difference equations.