Lectures on the Theory of Group Properties of Differential Equations

These lecturers provide a clear introduction to Lie group methods for determining and using symmetries of differential equations, a variety of their applications in gas dynamics and other nonlinear models as well as the author's remarkable contribution to this classical subject. It contains material that is useful for students and teachers but cannot be found in modern texts. For example, the theory of partially invariant solutions developed by Ovsyannikov provides a powerful tool for solving systems of nonlinear differential equations and investigating complicated mathematical models.
Contents:One-Parameter Continuous Transformation Groups Admitted by Differential Equations:One-Parameter Continuous Transformation GroupInfinitesimal Operator of the GroupInvariants and Invariant ManifoldsTheory of ProlongationGroups Admitted by Differential EquationsLie Algebra of OperatorsLie Algebras and Local Lie Groups:Lie AlgebraAdjoint AlgebraLocal Lie GroupSubgroup, Normal Subgroup and Factor GroupInner Automorphisms of a Group and of Its Lie AlgebraLocal Lie Group of TransformationsGroup Invariant Solutions of Differential Equations:Invariants of the Group GNrInvariant ManifoldsInvariant Solutions of Differential EquationsClassification of Invariant SolutionsPartially Invariant SolutionsReduction of Partially Invariant SolutionsSome Problems
Readership: Professional mathematics researchers and graduate students.