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Series on Soviet & East European Mathematics - Vol. 9
LECTURE NOTES ON GEOMETRICAL ASPECTS OF PARTIAL DIFFERENTIAL EQUATIONS
by V V Zharinov (Steklov Mathematical Institute)
This book focuses on the properties of nonlinear systems of PDE with geometrical origin and the natural description in the language of infinite-dimensional differential geometry. The treatment is very informal and the theory is illustrated by various examples from mathematical physics. All necessary information about the infinite-dimensional geometry is given in the text.
Contents:
- Introduction
- Internal Geometry of PDE:
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Differential Manifolds
- Lie-Backlund Mappings
- Lie-Backlund Fields and Infinitesimal Symmetries
- Cartan Forms, Currents and Conservation Laws
- C-Spectral Sequence. Further Properties of Conservation Laws
- Trivial Equations. The Formal Variational Calculus
- Evolution Equations
- External Geometry of PDE:
- Differential Submanifolds
- Normal Projection. External Fields and Forms
- Trivial Ambient Differential Manifolds
- The Characteristic Mapping
- The Green's Formula
- Low-Dimensional Conservation Laws
- Backlund Correspondence
- Further Studies:
- Lagrangian Formalism
- Hamiltonian Equations
- Example: The Nambu's String
- Appendix
Readership: Graduate students and researchers in mathematical physics.
| 372pp |
Pub. date: Mar 1992 |
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