Water Waves, Hamiltonian Systems and Cauchy Integrals

  • Walter Craig
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 30)


I will speak today about a classical fluid dynamical problem involving a free surface, the problem known as water waves. The results I want to describe are simply the derivation of a formalism that arises in posing the problem. This consists in writing the equations of motion as a Hamiltonian system. In doing this, several interesting questions arise, which are associated with Laplace’s equation on plane domains. I am not reporting on analytical results, rather this talk should be taken as a description of a point of view, or a set of coordinates that have a certain elegance.


Hamiltonian System Wave Packet Water Wave Fluid Domain Christoffel Symbol 
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Copyright information

© Springer-Verlag New York, Inc. 1991

Authors and Affiliations

  • Walter Craig
    • 1
  1. 1.Department of MathematicsBrown UniversityProvidenceUSA

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