Elementary Lie Group Analysis and Ordinary Differential Equations
Title | Elementary Lie Group Analysis and Ordinary Differential Equations PDF eBook |
Author | Nailʹ Khaĭrullovich Ibragimov |
Publisher | |
Total Pages | 347 |
Release | 1999 |
Genre | Differential equations |
ISBN |
Elementary Lie Group Analysis and Ordinary Differential Equations
Title | Elementary Lie Group Analysis and Ordinary Differential Equations PDF eBook |
Author | Nailʹ Khaĭrullovich Ibragimov |
Publisher | John Wiley & Sons |
Total Pages | 376 |
Release | 1999-05-04 |
Genre | Mathematics |
ISBN |
Lie group analysis, based on symmetry and invariance principles, is the only systematic method for solving nonlinear differential equations analytically. One of Lie's striking achievements was the discovery that the majority of classical devices for integration of special types of ordinary differential equations could be explained and deduced by his theory. Moreover, this theory provides a universal tool for tackling considerable numbers of differential equations when other means of integration fail. * This is the first modern text on ordinary differential equations where the basic integration methods are derived from Lie group theory * Includes a concise and self contained introduction to differential equations * Easy to follow and comprehensive introduction to Lie group analysis * The methods described in this book have many applications The author provides students and their teachers with a flexible text for undergraduate and postgraduate courses, spanning a variety of topics from the basic theory through to its many applications. The philosophy of Lie groups has become an essential part of the mathematical culture for anyone investigating mathematical models of physical, engineering and natural problems.
Group Analysis of Differential Equations
Title | Group Analysis of Differential Equations PDF eBook |
Author | L. V. Ovsiannikov |
Publisher | Academic Press |
Total Pages | 433 |
Release | 2014-05-10 |
Genre | Mathematics |
ISBN | 1483219062 |
Group Analysis of Differential Equations provides a systematic exposition of the theory of Lie groups and Lie algebras and its application to creating algorithms for solving the problems of the group analysis of differential equations. This text is organized into eight chapters. Chapters I to III describe the one-parameter group with its tangential field of vectors. The nonstandard treatment of the Banach Lie groups is reviewed in Chapter IV, including a discussion of the complete theory of Lie group transformations. Chapters V and VI cover the construction of partial solution classes for the given differential equation with a known admitted group. The theory of differential invariants that is developed on an infinitesimal basis is elaborated in Chapter VII. The last chapter outlines the ways in which the methods of group analysis are used in special issues involving differential equations. This publication is a good source for students and specialists concerned with areas in which ordinary and partial differential equations play an important role.
CRC Handbook of Lie Group Analysis of Differential Equations
Title | CRC Handbook of Lie Group Analysis of Differential Equations PDF eBook |
Author | Nail H. Ibragimov |
Publisher | CRC Press |
Total Pages | 452 |
Release | 1993-10-20 |
Genre | Mathematics |
ISBN | 9780849344886 |
Today Lie group theoretical approach to differential equations has been extended to new situations and has become applicable to the majority of equations that frequently occur in applied sciences. Newly developed theoretical and computational methods are awaiting application. Students and applied scientists are expected to understand these methods. Volume 3 and the accompanying software allow readers to extend their knowledge of computational algebra. Written by the world's leading experts in the field, this up-to-date sourcebook covers topics such as Lie-Bäcklund, conditional and non-classical symmetries, approximate symmetry groups for equations with a small parameter, group analysis of differential equations with distributions, integro-differential equations, recursions, and symbolic software packages. The text provides an ideal introduction to the modern group analysis and addresses issues to both beginners and experienced researchers in the application of Lie group methods.
CRC Handbook of Lie Group Analysis of Differential Equations
Title | CRC Handbook of Lie Group Analysis of Differential Equations PDF eBook |
Author | Nail H. Ibragimov |
Publisher | CRC Press |
Total Pages | 572 |
Release | 1995-10-24 |
Genre | Mathematics |
ISBN | 9780849394195 |
Today Lie group theoretical approach to differential equations has been extended to new situations and has become applicable to the majority of equations that frequently occur in applied sciences. Newly developed theoretical and computational methods are awaiting application. Students and applied scientists are expected to understand these methods. Volume 3 and the accompanying software allow readers to extend their knowledge of computational algebra. Written by the world's leading experts in the field, this up-to-date sourcebook covers topics such as Lie-Bäcklund, conditional and non-classical symmetries, approximate symmetry groups for equations with a small parameter, group analysis of differential equations with distributions, integro-differential equations, recursions, and symbolic software packages. The text provides an ideal introduction to modern group analysis and addresses issues to both beginners and experienced researchers in the application of Lie group methods.
CRC Handbook of Lie Group Analysis of Differential Equations, Volume I
Title | CRC Handbook of Lie Group Analysis of Differential Equations, Volume I PDF eBook |
Author | Nail H. Ibragimov |
Publisher | CRC Press |
Total Pages | 444 |
Release | 2023-08-25 |
Genre | Mathematics |
ISBN | 1000941426 |
Today Lie group theoretical approach to differential equations has been extended to new situations and has become applicable to the majority of equations that frequently occur in applied sciences. Newly developed theoretical and computational methods are awaiting application. Students and applied scientists are expected to understand these methods. Volume 3 and the accompanying software allow readers to extend their knowledge of computational algebra. Written by the world's leading experts in the field, this up-to-date sourcebook covers topics such as Lie-Bäcklund, conditional and non-classical symmetries, approximate symmetry groups for equations with a small parameter, group analysis of differential equations with distributions, integro-differential equations, recursions, and symbolic software packages. The text provides an ideal introduction to the modern group analysis and addresses issues to both beginners and experienced researchers in the application of Lie group methods.
Applications of Lie Groups to Differential Equations
Title | Applications of Lie Groups to Differential Equations PDF eBook |
Author | Peter J. Olver |
Publisher | Springer Science & Business Media |
Total Pages | 524 |
Release | 2012-12-06 |
Genre | Mathematics |
ISBN | 1468402749 |
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.