Symmetries and Related Topics in Differential and Difference Equations PDF Download
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Author: David Blázquez-Sanz
Publisher: American Mathematical Soc.
ISBN: 0821882422
Category : Mathematics
Languages : en
Pages : 178
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Book Description
Author: David Blázquez-Sanz
Publisher: American Mathematical Soc.
ISBN: 0821882422
Category : Mathematics
Languages : en
Pages : 178
Get Book
Book Description
Author: David Blázquez-Sanz
Publisher: American Mathematical Soc.
ISBN: 0821868721
Category : Mathematics
Languages : en
Pages : 178
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Book Description
The papers collected here discuss topics such as Lie symmetries, equivalence transformations and differential invariants, group theoretical methods in linear equations, and the development of some geometrical methods in theoretical physics. The reader will find new results in symmetries of differential and difference equations, applications in classical and quantum mechanics, two fundamental problems of theoretical mechanics, and the mathematical nature of time in Lagrangian mechanics.
Author: Albert C. J. Luo
Publisher: Springer Nature
ISBN: 981164683X
Category : Mathematics
Languages : en
Pages : 287
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Book Description
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.
Author: Decio Levi
Publisher: Springer
ISBN: 3319566660
Category : Science
Languages : en
Pages : 435
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Book Description
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: Hans Stephani
Publisher: Cambridge University Press
ISBN: 9780521366892
Category : Differential equations
Languages : en
Pages : 278
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Book Description
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.
Author: Decio Levi
Publisher: Cambridge University Press
ISBN: 1139493841
Category : Mathematics
Languages : en
Pages : 361
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Book Description
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: Victor G. Kac
Publisher: Springer
ISBN: 3030013766
Category : Mathematics
Languages : en
Pages : 199
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Book Description
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.
Author: George W. Bluman
Publisher: Springer Science & Business Media
ISBN: 0387680284
Category : Mathematics
Languages : en
Pages : 415
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Book Description
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.
Author: Brian J. Cantwell
Publisher: Cambridge University Press
ISBN: 9781139431712
Category : Mathematics
Languages : en
Pages : 670
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Book Description
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.
Author: George Bluman
Publisher: Springer Science & Business Media
ISBN: 0387216499
Category : Mathematics
Languages : en
Pages : 425
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Book Description
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.
