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

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.

Apparatus of Group Analysis: 1 Infinitesimal Calculus of Symmetry Groups 2. Group Classification of Differential Equations 3. Invariance Principle in Linear Second-Order Partial Differential Equations 4. Huygens' Principle: Conformal Invariance, Darboux Transformation, and Coxeter Groups 5. Applications to Celestial Mechanics and Astrophysics 6. Utilization of Vessiot-Guldberg-Lie Algebra for Integration of Nonlinear Equations- Body of Results 7. Symmetry Groups and Fundamental Solutions for Linear Equations of Mathematical Physics 8. Classical Field Theory 9. Earth Sciences 10. Group Invariant and Numerical Solutions for Glaciomechanics and Related Problems 11. Incompressible Fluids 12. Boundary Layer Problems 13. Non-Newtonian Fluids 14. Elasticity and Plasticity 15. Magnetohydrodynamics 16. Plasma Theory- Vlasov-Maxwell and Related Equations 17. Nonlinear Optics and Acoustics 18. Liquid Crystals 19. Classical Heritage- On Integration of a Class of Linear Partial Differential Equations by Means of Definite Integrals