Symmetries And Applications Of Differential Equations

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Symmetries and Applications of Differential Equations

Albert C. J. Luo,Rafail K. Gazizov
Symmetries and Applications of Differential Equations Book PDF

Author : Albert C. J. Luo,Rafail K. Gazizov
Publisher : Springer Nature
Page : 287 pages
File Size : 53,5 Mb
Release : 2021-12-14
Category : Mathematics
ISBN : 9789811646836

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Symmetries and Applications of Differential Equations by Albert C. J. Luo,Rafail K. Gazizov Pdf

This book is about Lie group analysis of differential equations for physical and engineering problems. The topics include: -- Approximate symmetry in nonlinear physical problems -- Complex methods for Lie symmetry analysis -- Lie group classification, Symmetry analysis, and conservation laws -- Conservative difference schemes -- Hamiltonian structure and conservation laws of three-dimensional linear elasticity -- Involutive systems of partial differential equations This collection of works is written in memory of Professor Nail H. Ibragimov (1939–2018). It could be used as a reference book in differential equations in mathematics, mechanical, and electrical engineering.

Differential Equations

Hans Stephani
Differential Equations Book PDF

Author : Hans Stephani
Publisher : Cambridge University Press
Page : 278 pages
File Size : 52,5 Mb
Release : 1989
Category : Differential equations
ISBN : 0521366895

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Differential Equations by Hans Stephani Pdf

This book provides an introduction to the theory and application of the solution to differential equations using symmetries, a technique of great value in mathematics and the physical sciences. It will apply to graduate students in physics, applied mathematics, and engineering.

Applications of Lie Groups to Differential Equations

Peter J. Olver
Applications of Lie Groups to Differential Equations Book PDF

Author : Peter J. Olver
Publisher : Springer Science & Business Media
Page : 524 pages
File Size : 45,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468402742

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Applications of Lie Groups to Differential Equations by Peter J. Olver Pdf

This book is devoted to explaining a wide range of applications of con tinuous symmetry groups to physically important systems of differential equations. Emphasis is placed on significant applications of group-theoretic methods, organized so that the applied reader can readily learn the basic computational techniques required for genuine physical problems. The first chapter collects together (but does not prove) those aspects of Lie group theory which are of importance to differential equations. Applications covered in the body of the book include calculation of symmetry groups of differential equations, integration of ordinary differential equations, including special techniques for Euler-Lagrange equations or Hamiltonian systems, differential invariants and construction of equations with pre scribed symmetry groups, group-invariant solutions of partial differential equations, dimensional analysis, and the connections between conservation laws and symmetry groups. Generalizations of the basic symmetry group concept, and applications to conservation laws, integrability conditions, completely integrable systems and soliton equations, and bi-Hamiltonian systems are covered in detail. The exposition is reasonably self-contained, and supplemented by numerous examples of direct physical importance, chosen from classical mechanics, fluid mechanics, elasticity and other applied areas.

Symmetries, Differential Equations and Applications

Victor G. Kac,Peter J. Olver,Pavel Winternitz,Teoman Özer
Symmetries Differential Equations and Applications Book PDF

Author : Victor G. Kac,Peter J. Olver,Pavel Winternitz,Teoman Özer
Publisher : Springer
Page : 199 pages
File Size : 51,6 Mb
Release : 2018-11-04
Category : Mathematics
ISBN : 9783030013769

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Symmetries, Differential Equations and Applications by Victor G. Kac,Peter J. Olver,Pavel Winternitz,Teoman Özer Pdf

Based on the third International Conference on Symmetries, Differential Equations and Applications (SDEA-III), this proceedings volume highlights recent important advances and trends in the applications of Lie groups, including a broad area of topics in interdisciplinary studies, ranging from mathematical physics to financial mathematics. The selected and peer-reviewed contributions gathered here cover Lie theory and symmetry methods in differential equations, Lie algebras and Lie pseudogroups, super-symmetry and super-integrability, representation theory of Lie algebras, classification problems, conservation laws, and geometrical methods. The SDEA III, held in honour of the Centenary of Noether’s Theorem, proven by the prominent German mathematician Emmy Noether, at Istanbul Technical University in August 2017 provided a productive forum for academic researchers, both junior and senior, and students to discuss and share the latest developments in the theory and applications of Lie symmetry groups. This work has an interdisciplinary appeal and will be a valuable read for researchers in mathematics, mechanics, physics, engineering, medicine and finance.

Applications of Symmetry Methods to Partial Differential Equations

George W. Bluman,Alexei F. Cheviakov,Stephen Anco
Applications of Symmetry Methods to Partial Differential Equations Book PDF

Author : George W. Bluman,Alexei F. Cheviakov,Stephen Anco
Publisher : Springer Science & Business Media
Page : 415 pages
File Size : 53,5 Mb
Release : 2009-10-30
Category : Mathematics
ISBN : 9780387680286

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Applications of Symmetry Methods to Partial Differential Equations by George W. Bluman,Alexei F. Cheviakov,Stephen Anco Pdf

This is an acessible book on the advanced symmetry methods for differential equations, including such subjects as conservation laws, Lie-Bäcklund symmetries, contact transformations, adjoint symmetries, Nöther's Theorem, mappings with some modification, potential symmetries, nonlocal symmetries, nonlocal mappings, and non-classical method. Of use to graduate students and researchers in mathematics and physics.

Symmetry Analysis of Differential Equations with Mathematica®

Gerd Baumann
Symmetry Analysis of Differential Equations with Mathematica Book PDF

Author : Gerd Baumann
Publisher : Springer Science & Business Media
Page : 532 pages
File Size : 49,5 Mb
Release : 2013-11-21
Category : Mathematics
ISBN : 9781461221104

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Symmetry Analysis of Differential Equations with Mathematica® by Gerd Baumann Pdf

The first book to explicitly use Mathematica so as to allow researchers and students to more easily compute and solve almost any kind of differential equation using Lie's theory. Previously time-consuming and cumbersome calculations are now much more easily and quickly performed using the Mathematica computer algebra software. The material in this book, and on the accompanying CD-ROM, will be of interest to a broad group of scientists, mathematicians and engineers involved in dealing with symmetry analysis of differential equations. Each section of the book starts with a theoretical discussion of the material, then shows the application in connection with Mathematica. The cross-platform CD-ROM contains Mathematica (version 3.0) notebooks which allow users to directly interact with the code presented within the book. In addition, the author's proprietary "MathLie" software is included, so users can readily learn to use this powerful tool in regard to performing algebraic computations.

Symmetries and Differential Equations

George W. Bluman,Sukeyuki Kumei
Symmetries and Differential Equations Book PDF

Author : George W. Bluman,Sukeyuki Kumei
Publisher : Springer Science & Business Media
Page : 424 pages
File Size : 43,8 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9781475743074

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Symmetries and Differential Equations by George W. Bluman,Sukeyuki Kumei Pdf

A major portion of this book discusses work which has appeared since the publication of the book Similarity Methods for Differential Equations, Springer-Verlag, 1974, by the first author and J.D. Cole. The present book also includes a thorough and comprehensive treatment of Lie groups of tranformations and their various uses for solving ordinary and partial differential equations. No knowledge of group theory is assumed. Emphasis is placed on explicit computational algorithms to discover symmetries admitted by differential equations and to construct solutions resulting from symmetries. This book should be particularly suitable for physicists, applied mathematicians, and engineers. Almost all of the examples are taken from physical and engineering problems including those concerned with heat conduction, wave propagation, and fluid flows. A preliminary version was used as lecture notes for a two-semester course taught by the first author at the University of British Columbia in 1987-88 to graduate and senior undergraduate students in applied mathematics and physics. Chapters 1 to 4 encompass basic material. More specialized topics are covered in Chapters 5 to 7.

Symmetry Methods for Differential Equations

Peter Ellsworth Hydon
Symmetry Methods for Differential Equations Book PDF

Author : Peter Ellsworth Hydon
Publisher : Cambridge University Press
Page : 230 pages
File Size : 44,6 Mb
Release : 2000-01-28
Category : Mathematics
ISBN : 0521497868

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Symmetry Methods for Differential Equations by Peter Ellsworth Hydon Pdf

This book is a straightforward introduction to the subject of symmetry methods for solving differential equations, and is aimed at applied mathematicians, physicists, and engineers. The presentation is informal, using many worked examples to illustrate the main symmetry methods. It is written at a level suitable for postgraduates and advanced undergraduates, and is designed to enable the reader to master the main techniques quickly and easily.The book contains some methods that have not previously appeared in a text. These include methods for obtaining discrete symmetries and integrating factors.

Symmetries and Applications of Differential Equations

Albert C. J. Luo,Rafail K. Gazizov
Symmetries and Applications of Differential Equations Book PDF

Author : Albert C. J. Luo,Rafail K. Gazizov
Publisher : Unknown
Page : 0 pages
File Size : 52,5 Mb
Release : 2021
Category : Electronic
ISBN : 9811646848

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Symmetries and Applications of Differential Equations by Albert C. J. Luo,Rafail K. Gazizov Pdf

This book is about Lie group analysis of differential equations for physical and engineering problems. The topics include: -- Approximate symmetry in nonlinear physical problems -- Complex methods for Lie symmetry analysis -- Lie group classification, Symmetry analysis, and conservation laws -- Conservative difference schemes -- Hamiltonian structure and conservation laws of three-dimensional linear elasticity -- Involutive systems of partial differential equations This collection of works is written in memory of Professor Nail H. Ibragimov (1939-2018). It could be used as a reference book in differential equations in mathematics, mechanical, and electrical engineering.

Symmetries of Partial Differential Equations

A.M. Vinogradov
Symmetries of Partial Differential Equations Book PDF

Author : A.M. Vinogradov
Publisher : Springer Science & Business Media
Page : 454 pages
File Size : 44,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400919488

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Symmetries of Partial Differential Equations by A.M. Vinogradov Pdf

2 The authors of these issues involve not only mathematicians, but also speci alists in (mathematical) physics and computer sciences. So here the reader will find different points of view and approaches to the considered field. A. M. VINOGRADOV 3 Acta Applicandae Mathematicae 15: 3-21, 1989. © 1989 Kluwer Academic Publishers. Symmetries and Conservation Laws of Partial Differential Equations: Basic Notions and Results A. M. VINOORADOV Department of Mathematics, Moscow State University, 117234, Moscow, U. S. S. R. (Received: 22 August 1988) Abstract. The main notions and results which are necessary for finding higher symmetries and conservation laws for general systems of partial differential equations are given. These constitute the starting point for the subsequent papers of this volume. Some problems are also discussed. AMS subject classifications (1980). 35A30, 58005, 58035, 58H05. Key words. Higher symmetries, conservation laws, partial differential equations, infinitely prolonged equations, generating functions. o. Introduction In this paper we present the basic notions and results from the general theory of local symmetries and conservation laws of partial differential equations. More exactly, we will focus our attention on the main conceptual points as well as on the problem of how to find all higher symmetries and conservation laws for a given system of partial differential equations. Also, some general views and perspectives will be discussed.

Introduction to Symmetry Analysis

Brian J. Cantwell
Introduction to Symmetry Analysis Book PDF

Author : Brian J. Cantwell
Publisher : Cambridge University Press
Page : 670 pages
File Size : 43,5 Mb
Release : 2002-09-23
Category : Mathematics
ISBN : 1139431714

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Introduction to Symmetry Analysis by Brian J. Cantwell Pdf

Symmetry analysis based on Lie group theory is the most important method for solving nonlinear problems aside from numerical computation. The method can be used to find the symmetries of almost any system of differential equations and the knowledge of these symmetries can be used to reduce the complexity of physical problems governed by the equations. This is a broad, self-contained, introduction to the basics of symmetry analysis for first and second year graduate students in science, engineering and applied mathematics. Mathematica-based software for finding the Lie point symmetries and Lie-Bäcklund symmetries of differential equations is included on a CD along with more than forty sample notebooks illustrating applications ranging from simple, low order, ordinary differential equations to complex systems of partial differential equations. MathReader 4.0 is included to let the user read the sample notebooks and follow the procedure used to find symmetries.

Continuous Symmetries, Lie Algebras, Differential Equations And Computer Algebra (2nd Edition)

Willi-hans Steeb
Continuous Symmetries Lie Algebras Differential Equations And Computer Algebra 2nd Edition Book PDF

Author : Willi-hans Steeb
Publisher : World Scientific Publishing Company
Page : 472 pages
File Size : 47,6 Mb
Release : 2007-07-26
Category : Science
ISBN : 9789813107014

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Continuous Symmetries, Lie Algebras, Differential Equations And Computer Algebra (2nd Edition) by Willi-hans Steeb Pdf

This textbook comprehensively introduces students and researchers to the application of continuous symmetries and their Lie algebras to ordinary and partial differential equations. Covering all the modern techniques in detail, it relates applications to cutting-edge research fields such as Yang-Mills theory and string theory.Aimed at readers in applied mathematics and physics rather than pure mathematics, the material is ideally suited to students and researchers whose main interest lies in finding solutions to differential equations and invariants of maps.A large number of worked examples and challenging exercises help readers to work independently of teachers, and by including SymbolicC++ implementations of the techniques in each chapter, the book takes full advantage of the advancements in algebraic computation.Twelve new sections have been added in this edition, including: Haar measure, Sato's theory and sigma functions, universal algebra, anti-self dual Yang-Mills equation, and discrete Painlevé equations.

Symmetry and Integration Methods for Differential Equations

George Bluman,Stephen Anco
Symmetry and Integration Methods for Differential Equations Book PDF

Author : George Bluman,Stephen Anco
Publisher : Springer Science & Business Media
Page : 422 pages
File Size : 48,9 Mb
Release : 2008-01-10
Category : Mathematics
ISBN : 9780387216492

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Symmetry and Integration Methods for Differential Equations by George Bluman,Stephen Anco Pdf

This text discusses Lie groups of transformations and basic symmetry methods for solving ordinary and partial differential equations. It places emphasis on explicit computational algorithms to discover symmetries admitted by differential equations and to construct solutions resulting from symmetries. This new edition covers contact transformations, Lie-B cklund transformations, and adjoints and integrating factors for ODEs of arbitrary order.

Continuous Symmetries, Lie Algebras, Differential Equations, and Computer Algebra

W.-H. Steeb
Continuous Symmetries Lie Algebras Differential Equations and Computer Algebra Book PDF

Author : W.-H. Steeb
Publisher : World Scientific
Page : 380 pages
File Size : 52,7 Mb
Release : 1996
Category : Science
ISBN : 9810228910

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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.

Similarity and Symmetry Methods

Jean-François Ganghoffer,Ivaïlo Mladenov
Similarity and Symmetry Methods Book PDF

Author : Jean-François Ganghoffer,Ivaïlo Mladenov
Publisher : Springer
Page : 380 pages
File Size : 48,8 Mb
Release : 2014-07-19
Category : Science
ISBN : 9783319082967

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Similarity and Symmetry Methods by Jean-François Ganghoffer,Ivaïlo Mladenov Pdf

The principle aim of the book is to present a self-contained, modern account of similarity and symmetry methods, which are important mathematical tools for both physicists, engineers and applied mathematicians. The idea is to provide a balanced presentation of the mathematical techniques and applications of symmetry methods in mathematics, physics and engineering. That is why it includes recent developments and many examples in finding systematically conservation laws, local and nonlocal symmetries for ordinary and partial differential equations. The role of continuous symmetries in classical and quantum field theories is exposed at a technical level accessible even for non specialists. The importance of symmetries in continuum mechanics and mechanics of materials is highlighted through recent developments, such as the construction of constitutive models for various materials combining Lie symmetries with experimental data. As a whole this book is a unique collection of contributions from experts in the field, including specialists in the mathematical treatment of symmetries, researchers using symmetries from a fundamental, applied or numerical viewpoint. The book is a fascinating overview of symmetry methods aimed for graduate students in physics, mathematics and engineering, as well as researchers either willing to enter in the field or to capture recent developments and applications of symmetry methods in different scientific fields.