Variational derivation of KdV-type of models for surface water waves

Embrecht W.C. van Groesen, A. Andonowati

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    18 Citations (Scopus)

    Abstract

    Using the Hamiltonian formulation of surface waves, we approximate the kinetic energy and restrict the governing generalized action principle to a submanifold of uni-directional waves. Different from the usual method of using a series expansion in parameters related to wave height and wavelength, the variational methods retains the Hamiltonian structure (with consequent energy and momentum conservation) and makes it possible to derive equations for any dispersive approximation. Consequentially, the procedure is valid for waves above finite and above infinite depth, and for any approximation of dispersion, while quadratic terms in the wave height are modeled correctly. For finite depth this leads to higher-order KdV type of equations with terms of different spatial order. For waves above infinite depth, the pseudo-differential operators cannot be approximated by finite differential operators and all quadratic terms are of the same spatial order.
    Original languageUndefined
    Article number10.1016/j.physleta.2007.02.031
    Pages (from-to)195-201
    Number of pages7
    JournalPhysics letters A
    Volume366
    Issue number06472
    DOIs
    Publication statusPublished - 2007

    Keywords

    • EWI-10240
    • METIS-241662
    • Finite and infinite depth
    • Hamiltonian formulation
    • Second-order nonlinear accurate
    • IR-61745
    • KdV equations

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