Lecture Notes On Geometrical Aspects Of Partial Differential Equations
World Scientific Publishing Co Pte Ltd (Verlag)
978-981-02-0753-3 (ISBN)
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.
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.
| Erscheint lt. Verlag | 1.3.1992 |
|---|---|
| Reihe/Serie | Series On Soviet And East European Mathematics ; 9 |
| Verlagsort | Singapore |
| Sprache | englisch |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-10 | 981-02-0753-0 / 9810207530 |
| ISBN-13 | 978-981-02-0753-3 / 9789810207533 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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