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.


Free Surface Hamiltonian System Water Wave Symplectic Form Symplectic Structure 
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© Springer Science + Business Media B.V 2008

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  • Walter Craig

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