Variational derivation of improved KP-type of equations

L.S.L. Lie She Liam, Embrecht W.C. van Groesen

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    Abstract

    The Kadomtsev–Petviashvili equation describes nonlinear dispersive waves which travel mainly in one direction, generalizing the Korteweg–de Vries equation for purely uni-directional waves. In this Letter we derive an improved KP-equation that has exact dispersion in the main propagation direction and that is accurate in second order of the wave height. Moreover, different from the KP-equation, this new equation is also valid for waves on deep water. These properties are inherited from the AB-equation (E. van Groesen, Andonowati, 2007 [1]) which is the unidirectional improvement of the KdV equation. The derivation of the equation uses the variational formulation of surface water waves, and inherits the basic Hamiltonian structure.
    Original languageUndefined
    Pages (from-to)411-415
    Number of pages5
    JournalPhysics letters A
    Volume374
    Issue number3
    DOIs
    Publication statusPublished - 4 Jan 2010

    Keywords

    • EWI-17265
    • Hamiltonian structure
    • KP-equation
    • Exact dispersion
    • METIS-270715
    • IR-69649
    • AB-equation
    • Surface water waves

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