Lecture notes on geometrical aspects of partial differential equations
著者
書誌事項
Lecture notes on geometrical aspects of partial differential equations
（Series on Soviet and East European mathematics, v. 9）
World Scientific, c1992
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注記
Bibliography: p. 351-356
Includes index
内容説明・目次
内容説明
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.
目次
- Part 1: Infinite dimensional manifolds. Part 2 Differential manifolds and PDE: Cartan distributions and differential manifolds
- Lie-Backlund mappings and symmetry groups
- Lie-Backlund fields and infinitesimal symmetries
- Cartan forms, currents and conservation laws
- c-spectral sequence. Part 3 External geometry: Backlund correspondence
- differential submanifolds and the normal projection
- external fields and forms
- Green's formula
- characteristic mapping. Part 4 Examples: trivial equations
- evolution equations
- Cauchy-Kowalevsky equations
- Hamiltonian equations
- Euler-Lagrange equations
- Noether theorem
- the classical relativistic string. Part 5 Differential algebras and PDE: differential algebras
- fields, forms and differential operators
- resolutions of differential algebras
- differential ideals
- conservation laws of lower dimensions.
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