The volume consists of three parts. Part A is a conceptual introduction to the group analysis of differential equations. It is devoted to a systematization of relevant results of S. Lie and their generalizations. This part is an excellent guide to researchers and graduate students in the group analysis methods of differential equations. Part B contains results of group analysis of concrete differential equations. Their group classifications, classical, higher, and nonlocal symmetries, Bäcklund transformations, exact solutions, and conservation laws are tabulated here. Part C is devoted to numerical computer aspects of the group analysis of differential equations. The book is very useful as a reference for experts in the group analysis of differential equations.
Contents: Preface. Part A. Apparatus of group analysis. I. Lie theory of differential equations. One-parameter transformation group. Integration of the second order ordinary differential equations. Group classification of second-order ordinary differential equations. Invariant solutions. II. Generalizations. Lie-Bäcklund transformation groups. Noether-type conservation theorems. Nonlocal symmetry generators via Bäcklund transformations.
Part B. Body of results. Ordinary differential equations. Second-order PDE with two independent variables. Evolution equations I: Diffusion equations. Evolution equations II: General case. Wave equations. Hydrodynamics and gasdynamics. Hydrodynamics-type systems. Integrodifferential equations.
Part C. Computer aspects. Application of group theory in computation – a survey. Symmetry of finite-difference equations.