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Viser: Applications of Lie Groups to Differential Equations
Applications of Lie Groups to Differential Equations
Peter J. Olver
(2000)
Sprog: Engelsk
Detaljer om varen
- 2. Udgave
- Paperback
- Udgiver: Springer New York (Januar 2000)
- ISBN: 9780387950006
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. Noether's Theorem.- Notes.- Exercises.- 5 Generalized Symmetries.-
5.1. Generalized Symmetries of Differential Equations.-
5.2. Récursion Operators, Master Symmetries and Formal Symmetries.-
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.