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Transformation theory of Hamiltonian PDE and the problem of water waves

  • Walter Craig
Part of the NATO Science for Peace and Security Series book series (NAPSB)

This set of lecture notes gives (i) a formal theory of Hamiltonian systems posed in infinite dimensions, (ii) a perturbation theory in the presence of a small parameter, adapted to reproduce some of the well-known formal computations of fluid mechanics, and (iii) a transformation theory of Hamiltonian systems and their symplectic structures. A series of examples is given, starting with a rather complete description of the problem of water waves, and, following a series of scaling and other simple transformations placed in the above context, a derivation of the well known equations of Boussinesq and Korteweg de Vries.

Keywords

Free Surface Hamiltonian System Water Wave Symplectic Form Symplectic Structure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer Science + Business Media B.V 2008

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  • Walter Craig

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