Continuous Symmetries And Integrability Of Discrete Equations

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Continuous Symmetries And Integrability Of Discrete Equations

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Author : Decio Levi
language : en
Publisher: American Mathematical Society, Centre de Recherches Mathématiques
Release Date : 2023-01-23

Continuous Symmetries And Integrability Of Discrete Equations written by Decio Levi and has been published by American Mathematical Society, Centre de Recherches Mathématiques this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-23 with Mathematics categories.

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.

Side Iii Symmetries And Integrability Of Difference Equations

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Author : D. Levi
language : en
Publisher: American Mathematical Soc.
Release Date : 2000

Side Iii Symmetries And Integrability Of Difference Equations written by D. Levi and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.

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.

Symmetries And Integrability Of Difference Equations

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Author : Decio Levi
language : en
Publisher: American Mathematical Soc.
Release Date :

Symmetries And Integrability Of Difference Equations written by Decio Levi and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.

Symmetries And Integrability Of Difference Equations

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Author : Peter A. Clarkson
language : en
Publisher: Cambridge University Press
Release Date : 1999-02-04

Symmetries And Integrability Of Difference Equations written by Peter A. Clarkson and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-02-04 with Mathematics categories.

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

Difference And Differential Equations

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Author : Saber Elaydi
language : en
Publisher: American Mathematical Soc.
Release Date : 2004

Difference And Differential Equations written by Saber Elaydi and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.

Contains papers from the 7th International Conference on Difference Equations held at Hunan University (Changsa, China), a satellite conference of ICM2002 Beijing. This book includes articles that cover stability, chaos, symmetries, boundary value problems and bifurcations for discrete dynamical systems, and difference-differential equations.

Discrete Systems And Integrability

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Author : J. Hietarinta
language : en
Publisher: Cambridge University Press
Release Date : 2016-09

Discrete Systems And Integrability written by J. Hietarinta and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09 with Mathematics categories.

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

Difference Equations Special Functions And Orthogonal Polynomials

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Author : Saber Elaydi
language : en
Publisher: World Scientific
Release Date : 2007

Difference Equations Special Functions And Orthogonal Polynomials written by Saber Elaydi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Science categories.

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.

Difference Equations Special Functions And Orthogonal Polynomials Proceedings Of The International Conference

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Author : Jim M Cushing
language : en
Publisher: World Scientific
Release Date : 2007-05-21

Difference Equations Special Functions And Orthogonal Polynomials Proceedings Of The International Conference written by Jim M Cushing and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-21 with Mathematics categories.

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.

The Geometrical Study Of Differential Equations

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Author : Joshua Allensworth Leslie
language : en
Publisher: American Mathematical Soc.
Release Date : 2001

The Geometrical Study Of Differential Equations written by Joshua Allensworth Leslie and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.

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.

Mathematical Models And Integration Methods

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Author : Oleg V. Kaptsov
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2024-09-23

Mathematical Models And Integration Methods written by Oleg V. Kaptsov and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-23 with Mathematics categories.

The book compiles works presented at a seminar aiming to attract global experts in differential equations, mathematical modeling, and integration methods. It covers classical and contemporary integration techniques for partial differential equations, including Monge and Darboux's approaches and their extensions. Additionally, it introduces a novel theoretical model for plane turbulent flows, presents gravitational equations derived from the principle of least action, and explores symmetry-preserving conservative finite-difference schemes for hydrodynamic-type equations. Analytical solutions for Maxwell's equations in incompressible viscoelastic mediums are examined, alongside theoretical-group analysis of wake mathematical models and reduction to ordinary differential equations. The book also delves into special classes of two-dimensional ideal fluid motion and advancements in discrete orthogonal polynomial theory, showcasing rapid decay properties near interval boundaries. In conclusion, this comprehensive collection is indispensable for researchers and practitioners in applied mathematics, fluid dynamics, and computational modeling, providing valuable insights into cutting-edge methods and solutions in the field.