1st Edition

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

By Nail H. Ibragimov Copyright 1995
    552 Pages
    by CRC Press

    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.

    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


    Ibragimov, Nail H.

    "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