Solitons and geometry
著者
書誌事項
Solitons and geometry
（Pubblicazioni della Classe di scienze / Scuola Normale Superiore, Lezioni fermiane）
Published for the Accademia nazionale dei Lincei and the Scuola normale superiore by the Press Syndicate of the University of Cambridge, 1994
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注記
"Pisa, 1992"
At head title: Accademia nazionale dei Lincei. Scuola normale superiore
内容説明・目次
内容説明
This is an introduction to the geometry of Hamiltonian systems from the modern point of view where the basic structure is a Poisson bracket. Using this approach a mathematical analogue of the famous 'Dirac monopole' is obtained starting from the classical top in a gravity field. This approach is especially useful in physical applications in which a field theory appears; this is the subject of the second part of the lectures, which contains a theory of conservative hydrodynamic-type systems, based on Riemannian geometry, developed over the last decade. The theory has had success in solving problems in physics, such as ones associated with dispersive analogues of shock waves, and its development has led to the introduction of new notions in geometry. The book is based on lectures given by the author in Pisa and which were intended for a non-specialist audience. It provides an introduction from which to proceed to more advanced work in the area.
目次
- 1. Introduction, plan of the lectures, Poisson structures
- 2. Poisson structures on finite-dimensional manifolds, Hamiltonian systems, completely integrable systems
- 3. Classical analogue of the Dirac monopole, complete integrability and algebraic geometry
- 4. Poisson structures on loop spaces, systems of hydrodynamic type and differential geometry
- 5. Non-linear WKB method, hydrodynamics of weakly deformed soliton lattices
- References.
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