Author | Olver, Peter J. author |
---|---|
Title | Applications of Lie Groups to Differential Equations [electronic resource] / by Peter J. Olver |
Imprint | New York, NY : Springer US, 1986 |
Connect to | http://dx.doi.org/10.1007/978-1-4684-0274-2 |
Descript | online resource |
1 Introduction to Lie Groups -- 1.1. Manifolds -- 1.2. Lie Groups -- 1.3. Vector Fields -- 1.4. Lie Algebras -- 1.5. Differential Forms -- Notes -- Exercises -- 2 Symmetry Groups of Differential Equations -- 2.1. Symmetries of Algebraic Equations -- 2.2. Groups and Differential Equations -- 2.3. Prolongation -- 2.4. Calculation of Symmetry Groups -- 2.5. Integration of Ordinary Differential Equations -- 2.6. Nondegeneracy Conditions for Differential Equations -- Notes -- Exercises -- 3 Group-Invariant Solutions -- 3.1. Construction of Group-Invariant Solutions -- 3.2. Examples of Group-Invariant Solutions -- 3.3. Classification of Group-Invariant Solutions -- 3.4. Quotient Manifolds -- 3.5. Group-Invariant Prolongations and Reduction -- Notes -- Exercises -- 4 Symmetry Groups and Conservation Laws -- 4.1. The Calculus of Variations -- 4.2. Variational Symmetries -- 4.3. Conservation Laws -- 4.4. Noetherโs Theorem -- Notes -- Exercises -- 5 Generalized Symmetries -- 5.1. Generalized Symmetries of Differential Equations -- 5.2. Recursion Operators -- 5.3. Generalized Symmetries and Conservation Laws -- 5.4. The Variational Complex -- Notes -- Exercises -- 6 Finite-Dimensional Hamiltonian Systems -- 6.1. Poisson Brackets -- 6.2. Symplectic Structures and Foliations -- 6.3. Symmetries, First Integrals and Reduction of Order -- Notes -- Exercises -- 7 Hamiltonian Methods for Evolution Equations -- 7.1. Poisson Brackets -- 7.2. Symmetries and Conservation Laws -- 7.3. Bi-Hamiltonian Systems -- Notes -- Exercises -- References -- Symbol Index -- Author Index