Continuous Symmetries And Integrability Of Discrete Equations

Author : Decio Levi,Pavel Winternitz,Ravil I. Yamilov
Publisher : American Mathematical Society, Centre de Recherches Mathématiques
Page : 520 pages
File Size : 47,5 Mb
Release : 2023-01-23
Category : Mathematics
ISBN : 9780821843543

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Continuous Symmetries and Integrability of Discrete Equations by Decio Levi,Pavel Winternitz,Ravil I. Yamilov Pdf

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.

Author : Decio Levi,Peter Olver,Zora Thomova,Pavel Winternitz
Publisher : Cambridge University Press
Page : 361 pages
File Size : 41,6 Mb
Release : 2011-06-23
Category : Mathematics
ISBN : 9781139493840

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Symmetries and Integrability of Difference Equations by Decio Levi,Peter Olver,Zora Thomova,Pavel Winternitz Pdf

A comprehensive introduction to the subject suitable for graduate students and researchers. This book is also an up-to-date survey of the current state of the art and thus will serve as a valuable reference for specialists in the field.

Author : Decio Levi,Raphaël Rebelo,Pavel Winternitz
Publisher : Springer
Page : 435 pages
File Size : 47,6 Mb
Release : 2017-06-30
Category : Science
ISBN : 9783319566665

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Symmetries and Integrability of Difference Equations by Decio Levi,Raphaël Rebelo,Pavel Winternitz Pdf

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 : Decio Levi
Publisher : American Mathematical Soc.
Page : 462 pages
File Size : 52,7 Mb
Release : 2000
Category : Difference equations
ISBN : 9780821821282

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SIDE III -- Symmetries and Integrability of Difference Equations by Decio Levi Pdf

This volume contains the proceedings of the third meeting on "Symmetries and Integrability of Difference Equations" (SIDE III). The collection includes original results not published elsewhere and articles that give a rigorous but concise overview of their subject, and provides a complete description of the state of the art. Research in the field of difference equations-often referred to more generally as discrete systems-has undergone impressive development in recent years. In this collection the reader finds the most important new developments in a number of areas, including: Lie-type symmetries of differential-difference and difference-difference equations, integrability of fully discrete systems such as cellular automata, the connection between integrability and discrete geometry, the isomonodromy approach to discrete spectral problems and related discrete Painlevé equations, difference and q-difference equations and orthogonal polynomials, difference equations and quantum groups, and integrability and chaos in discrete-time dynamical systems. The proceedings will be valuable to mathematicians and theoretical physicists interested in the mathematical aspects and/or in the physical applications of discrete nonlinear dynamics, with special emphasis on the systems that can be integrated by analytic methods or at least admit special explicit solutions. The research in this volume will also be of interest to engineers working in discrete dynamics as well as to theoretical biologists and economists.

Author : J. Hietarinta,N. Joshi,F. W. Nijhoff
Publisher : Cambridge University Press
Page : 461 pages
File Size : 44,6 Mb
Release : 2016-09
Category : Mathematics
ISBN : 9781107042728

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Discrete Systems and Integrability by J. Hietarinta,N. Joshi,F. W. Nijhoff Pdf

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

Author : Anonim
Publisher : Unknown
Page : 388 pages
File Size : 43,5 Mb
Release : 1996
Category : Difference equations
ISBN : 1470439239

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Symmetries and Integrability of Difference Equations by Anonim Pdf

Author : Decio Levi,Luc Vinet,Pavel Winternitz
Publisher : American Mathematical Soc.
Page : 404 pages
File Size : 53,8 Mb
Release : 2024-06-14
Category : Mathematics
ISBN : 0821870505

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Symmetries and Integrability of Difference Equations by Decio Levi,Luc Vinet,Pavel Winternitz Pdf

Author : Anonim
Publisher : Unknown
Page : 444 pages
File Size : 55,6 Mb
Release : 2000
Category : Difference equations
ISBN : 1470439395

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SIDE III by Anonim Pdf

This volume contains the proceedings of the third meeting on "Symmetries and Integrability of Difference Equations" (SIDE III). The collection includes original results not published elsewhere and articles that give a rigorous but concise overview of their subject, and provides a complete description of the state of the art. Research in the field of difference equations-often referred to more generally as discrete systems-has undergone impressive development in recent years. In this collection the reader finds the most important new developments in a number of areas, including: Lie-type symmet.

Author : Decio Levi,Orlando Ragnisco
Publisher : American Mathematical Soc.
Page : 468 pages
File Size : 55,8 Mb
Release : 2000-06-15
Category : Mathematics
ISBN : 0821870211

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SIDE III by Decio Levi,Orlando Ragnisco Pdf

This volume contains the proceedings of the third meeting on ``Symmetries and Integrability of Difference Equations'' (SIDE III). The collection includes original results not published elsewhere and articles that give a rigorous but concise overview of their subject, and provides a complete description of the state of the art. Research in the field of difference equations--often referred to more generally as discrete systems--has undergone impressive development in recent years. In this collection the reader finds the most important new developments in a number of areas, including: Lie-type symmetries of differential-difference and difference-difference equations, integrability of fully discrete systems such as cellular automata, the connection between integrability and discrete geometry, the isomonodromy approach to discrete spectral problems and related discrete Painleve equations, difference and q-difference equations and orthogonal polynomials, difference equations and quantum groups, and integrability and chaos in discrete-time dynamical systems. The proceedings will be valuable to mathematicians and theoretical physicists interested in the mathematical aspects and/or in the physical applications of discrete nonlinear dynamics, with special emphasis on the systems that can be integrated by analytic methods or at least admit special explicit solutions. The research in this volume will also be of interest to engineers working in discrete dynamics as well as to theoretical biologists and economists.

Author : Peter A. Clarkson,Frank W. Nijhoff
Publisher : Cambridge University Press
Page : 444 pages
File Size : 49,8 Mb
Release : 1999-02-04
Category : Mathematics
ISBN : 0521596998

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Symmetries and Integrability of Difference Equations by Peter A. Clarkson,Frank W. Nijhoff Pdf

This volume comprises state-of-the-art articles in discrete integrable systems.

Author : Peter A. Clarkson,Frank W. Nijhoff
Publisher : Unknown
Page : 444 pages
File Size : 43,6 Mb
Release : 1999
Category : Difference equations
ISBN : 1107367506

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Symmetries and Integrability of Difference Equations by Peter A. Clarkson,Frank W. Nijhoff Pdf

This volume comprises state-of-the-art articles in discrete integrable systems.

Author : Saber Elaydi
Publisher : American Mathematical Soc.
Page : 452 pages
File Size : 51,7 Mb
Release : 2024-06-14
Category : Mathematics
ISBN : 0821871463

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Difference and Differential Equations by Saber Elaydi Pdf

This volume contains papers from the 7th International Conference on Difference Equations held at Hunan University (Changsa, China), a satellite conference of ICM2002 Beijing. The volume captures the spirit of the meeting and includes peer-reviewed survey papers, research papers, and open problems and conjectures. Articles cover stability, oscillation, chaos, symmetries, boundary value problems and bifurcations for discrete dynamical systems, difference-differential equations, and discretization of continuous systems. The book presents state-of-the-art research in these important areas. It is suitable for graduate students and researchers in difference equations and related topics.

Author : W-H Steeb
Publisher : World Scientific Publishing Company
Page : 372 pages
File Size : 46,5 Mb
Release : 1996-09-30
Category : Science
ISBN : 9789813105034

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Continuous Symmetries, Lie Algebras, Differential Equations and Computer Algebra by W-H Steeb Pdf

This book is a comprehensive introduction to the application of continuous symmetries and their Lie algebras to ordinary and partial differential equations. It is suitable for students and research workers whose main interest lies in finding solutions to differential equations. It therefore caters for readers primarily interested in applied mathematics and physics rather than pure mathematics. The book provides an application-orientated text that is reasonably self-contained. A large number of worked examples have been included to help readers working independently of a teacher. The advance of algebraic computation has made it possible to write programs for the tedious calculations in this research field, and thus the book also makes a survey of computer algebra packages.

Author : Joshua Allensworth Leslie,Thierry P. Robart
Publisher : American Mathematical Soc.
Page : 226 pages
File Size : 49,9 Mb
Release : 2001
Category : Differential equations
ISBN : 9780821829646

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The Geometrical Study of Differential Equations by Joshua Allensworth Leslie,Thierry P. Robart Pdf

This volume contains papers based on some of the talks given at the NSF-CBMS conference on ``The Geometrical Study of Differential Equations'' held at Howard University (Washington, DC). The collected papers present important recent developments in this area, including the treatment of nontransversal group actions in the theory of group invariant solutions of PDEs, a method for obtaining discrete symmetries of differential equations, the establishment of a group-invariant version of the variational complex based on a general moving frame construction, the introduction of a new variational complex for the calculus of difference equations and an original structural investigation of Lie-Backlund transformations. The book opens with a modern and illuminating overview of Lie's line-sphere correspondence and concludes with several interesting open problems arising from symmetry analysis of PDEs. It offers a rich source of inspiration for new or established researchers in the field. This book can serve nicely as a companion volume to a forthcoming book written by the principle speaker at the conference, Professor Niky Kamran, to be published in the AMS series, CBMS Regional Conference Series in Mathematics.

Author : Saber Elaydi
Publisher : World Scientific
Page : 789 pages
File Size : 54,9 Mb
Release : 2007
Category : Science
ISBN : 9789812770752

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Difference Equations, Special Functions and Orthogonal Polynomials by Saber Elaydi Pdf

This volume contains talks given at a joint meeting of three communities working in the fields of difference equations, special functions and applications (ISDE, OPSFA, and SIDE). The articles reflect the diversity of the topics in the meeting but have difference equations as common thread. Articles cover topics in difference equations, discrete dynamical systems, special functions, orthogonal polynomials, symmetries, and integrable difference equations.