Differential Equations: Their Solution Using Symmetries

ISBN: 9780521366892 出版年：1990 页码：274 Hans Stephani Malcolm MacCallum Cambridge University Press

Preface 1. Introduction Part I. Ordinary Differential Equations: 2. Point transformations and their generators 3. Lie point symmetries of ordinary differential equations: the basic definitions and properties 4. How to find the Lie point symmetries of an ordinary differential equation 5. How to use Lie point symmetries: differential equations with one symmetry 6. Some basic properties of Lie algebras 7. How to use Lie point symmetries: second order differential equations admitting a G2 8. Second order differential equations admitting a G3IX 9. Higher order differential equations admitting more than one Lie point symmetry 10 Systems of second order differential equations 11. Symmetries more general than Lie point symmetries 12. Dynamical symmetries: the basic definitions and properties 13. How to find and use dynamical symmetries for systems possessing a Lagrangian 14. Systems of first order differential equations with a fundamental system of solutions Part II. Partial Differential Equations: 15. Lie point transformations and symmetries 16. How to determine the point symmetries of partial differential equations 17. How to use Lie point symmetries of partial differential equations I: generating solutions by symmetry 18. How to use Lie point symmetries of partial differential equations II: similarity variables and reduction of the number of variables 19. How to use Lie point symmetries of partial differential equations III: multiple reduction of variables and differential invariants 20. Symmetries and the separability of partial differential classification 21. Contact transformations and contact symmetries of partial differential equations, and how to use them 22. Differential equations and symmetries in the language of forms 23. Lie-Backlund transformations 24. Lie-Backlund symmetries and how to find them 25. How to use Lie-Backlund symmetries Appendices Index.