Presents an introduction to the modern group analysis. This work covers topics such as Lie-Backlund, 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.
Presents an introduction to the modern group analysis. This work covers topics such as Lie-Backlund, 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.
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.
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.
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