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

by Nail H. Ibragimov

Overview

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.

Product Details

ISBN-13:	9781040295328
Publisher:	CRC Press
Publication date:	11/01/2024
Sold by:	Barnes & Noble
Format:	eBook
Pages:	552
File size:	1 MB

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 Recursions 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

Editorial Reviews

An introduction for beginners and a comprehensive reference for experienced researchers in Lie group analysis, presenting newly developed theoretical and computational methods. Explains the apparatus of group analysis from such perspectives as representation by formal power series, approximate transformation groups, and recursion. Reports results in group theoretic modeling, generalized hydrodynamic-type systems, nonclassical and conditional symmetries, and other areas. Also surveys computational methods that use symbolic software, and details the interactive REDUCE programs that are provided on a 3.5" disk. Apparently the final volume of the series. Annotation c. Book News, Inc., Portland, OR (booknews.com)

Booknews

"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

From the Publisher