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 the modern group analysis and addresses issues to both beginners and experienced researchers in the application of Lie group methods.
APPARATUS OF GROUP ANALYSIS: Lie Theory of Differential Equations: One Parameter Transformation Groups. Integration of Second-Order Ordinary Differential Equations. Group Classification of Second-Order Ordinary Differential Equations. Invariant Solutions. Generalizations: Lie-Bäcklund Transformation Groups. Noether-Type Conservation Theorems. Non-Local Symmetry Generators via Bäcklund Transformations. BODY OF RESULTS: Ordinary Differential Equations. Second Order Partial Differential Equations with Two Independent Variables. Evolution Equations I: Diffusion Equations. Evolution Equations II: General Case. Wave Equations. Hydro- and Gas- Dynamics. Hydrodynamic-Type Systems. Integrodifferential Equations. COMPUTER ASPECTS: Applications of Group Theory in Computation. Symmetry of Finite-Difference Equations. References. Indices.