Handbook of Lie Group Analysis of Differential Equations,
Volume 2: Applications in Engineering
and Physical Sciences

Editor - Nail H. Ibragimov

Insitute of Mathematical Modeling, Russian Academy of Sciences, Moscow, Russia

Description | Features | Contents | Audience | Publi cation Information and Price | Other Titles

Description

Volume 2 offers a unique blend of classical results of Sophus Lie with new, modern developments and numerous applications which span a period of more than 100 years. As a result, this reference is up to date, with the latest information on the group theoretic methods used frequently in mathematical physics and engineering.

Volume 2 is divided into three parts. Part A focuses on relevant definitions, main algorithms, group classification schemes for partial differential equations, and multifaceted possibilities offered by Lie group theoretic philosophy. Part B contains the group analysis of a variety of mathematical models for diverse natural phenomena. It tabulates symmetry groups and solutions for linear equations of mathematical physics, classical field theory, viscous and non-Newtonian fluids, boundary layer problems, Earth sciences, elasticity, plasticity, plasma theory (Vlasov-Maxwell equations), and nonlinear optics and acoustics. Part C offers an English translation of Sophus Lie's fundamental paper on the group classification and invariant solutions of linear second-order equations with two independent variables. This will serve as a concise, practical guide to the group analysis of partial differential equations.

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Features

• No other work offers such a unique blend of classical results and modern developments
• Concisely presents the relevant definitions and algorithms of Lie group analysis of differential equations required by applied scientists and engineers
• Provides a comprehensive listing of applications of Lie groups to differential equations which frequently occur in engineering and physical sciences
• Presented in an easy-to-follow, applications-oriented style

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Contents

Apparatus of Group Analysis

Infinitesimal Calculus of Symmetry Groups
Group Classification of Differential Equations
Invariance Principle in Linear Second-Order Partial Differential Equations
Huygens' Principle: Conformal Invariance, Darboux Transformation, and Coxeter Groups
Applications to Celestial Mechanics and Astrophysics
Utilization of Vessiot-Guldberg-Lie Algebra for Integration of Nonlinear Equations

Body of Results

Symmetry Groups and Fundamental Solutions for Linear Equations of Mathematical Physics
Classical Field Theory
Earth Sciences
Group Invariant and Numerical Solutions for Glaciomechanics and Related Problems
Incompressible Fluids
Boundary Layer Problems
Non-Newtonian Fluids
Elasticity and Plasticity
Magnetohydrodynamics
Plasma Theory: Vlasov-Maxwell and Related Equations
Nonlinear Optics and Acoustics
Liquid Crystals

Classical Heritage

On Integration of a Class of Linear Partial Differential Equations by Means of Definite Integrals
(S. Lie)

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Audience

Applied mathematicians, physicists, and engineers

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Publication and Pricing

Catalog no. 2864WGBA

November 1994, 576 pp., ISBN: 0-8493-2864-0

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Related Titles

Catalog 4488WCRL

CRC Handbook of Lie Group Analysis of Differential Equations, Volumes 1, 2, and 3
Editor - Nail H. Ibragimov, Department of Computational and Applied Mathematics, University of Witwatersrand, Johannesburg, South Africa

Catalog 9419WCRL

CRC Handbook of Lie Group Analysis of Differential Equations, Volume 3: New Trends in Theoretical Developments and Computational Methods
Editor - Nail H. Ibragimov, Department of Computational and Applied Mathematics, University of Witwatersrand, Johannesburg, South Africa

Catalog 7373WCRX

Computational Mathematics in Engineering and Applied Science by Schiesser