CRC Handbook of Lie Group Analysis of Differential Equations, Volume III: 1st Edition (Hardback) book cover

CRC Handbook of Lie Group Analysis of Differential Equations, Volume III

1st Edition

By Nail H. Ibragimov

CRC Press

560 pages

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Hardback: 9780849394195
pub: 1995-10-24
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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.


"This handbook is a welcome addition to the literature on the theory and applications of symmetries of differential equations…novel…insightful…valuable…a wealth of information."

- Juha Pohjanpelto, Oregon State University, Corvallis

Table of Contents

Apparatus of Group Analysis

Lie-Bäcklund Symmetries: Representation by Formal Power Series

Approximate Transformation Groups

Differential Equations with Distributions: Group Theoretic Treatment of Fundamental Solutions


Calculation of Symmetry Groups for Integro-Differential Equations

Body of Results

Group Theoretic Modeling

Generalized Hydrodynamic-Type Systems

Ordinary Differential Equations

Differential Equations with a Small Parameter: Exact and Approximate Symmetries

Differential Constraints

Non-Classical and Conditional Symmetries

Quasi-Exactly-Solvable Differential Equations

Computational Methods

Symbolic Software for Lie Symmetry Analysis

Interactive REDUCE Programs for Caculating Lie Point, Non-Classical, Lie-Bäcklund, and Approximate Symmetries of Differential Equations: Manual and Floppy Disk

About the Authors

Ibragimov, Nail H.

Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Algebra / General
MATHEMATICS / Differential Equations