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.
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
Non-Classical and Conditional Symmetries
Quasi-Exactly-Solvable Differential Equations
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
"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