Hamiltonian and non-Hamiltonian models for water waves

  • Peter J. Olver
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 195)


A general theory for determining Hamiltonian model equations from noncanonical perturbation expansions of Hamiltonian systems is applied to the Boussinesq expansion for long, small amplitude waves in shallow water, leading to the Korteweg-de-Vries equation.New Hamiltonian model equations, including a natural “Hamiltonian version” of the KdV equation, are proposed. The method also provides a direct explanation of the complete integrability (soliton property) of the KdV equation. Depth dependence in both the Hamiltonian models and the second order standard perturbation models is discussed as a possible mechanism for wave breaking.


Poisson Bracket Water Wave Hamiltonian Operator Solitary Wave Solution Perturbation Expansion 
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Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • Peter J. Olver
    • 1
  1. 1.School of MathematicsUniversity of MinnesotaMinneapolisUSA

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