Energy propagation in dissipative systems Part II: Centrovelocity for nonlinear wave equations

G.L.A. Derks, G. Derks, Embrecht W.C. van Groesen

    Research output: Contribution to journalArticleAcademicpeer-review

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    Abstract

    We consider nonlinear wave equations, first order in time, of a specific form. In the absence of dissipation, these equations are given by a Poisson system, with a Hamiltonian that is the integral of some density. The functional I, defined to be the integral of the square of the waveform, is a constant of motion of the unperturbed system. It will be shown that Z, the center of gravity of this density, is canonically conjugate to I and can be used as a measure to locate the position of the waveform. By introducing new coordinates based on Z, we get expressions for the centrovelocity, Image, and the decay of I, which compare to the ones of part I, in both the conservative and the dissipative case. With the derived expressions, we investigate the decay of solitary waves of the Korteweg-de Vries equation, when different kinds of dissipation are added.
    Original languageUndefined
    Pages (from-to)159-172
    Number of pages14
    JournalWave motion
    Volume0
    Issue number15
    DOIs
    Publication statusPublished - 1992

    Keywords

    • METIS-140893
    • IR-30253

    Cite this

    @article{b1e91d0d570440be8e845ae6387c0921,
    title = "Energy propagation in dissipative systems Part II: Centrovelocity for nonlinear wave equations",
    abstract = "We consider nonlinear wave equations, first order in time, of a specific form. In the absence of dissipation, these equations are given by a Poisson system, with a Hamiltonian that is the integral of some density. The functional I, defined to be the integral of the square of the waveform, is a constant of motion of the unperturbed system. It will be shown that Z, the center of gravity of this density, is canonically conjugate to I and can be used as a measure to locate the position of the waveform. By introducing new coordinates based on Z, we get expressions for the centrovelocity, Image, and the decay of I, which compare to the ones of part I, in both the conservative and the dissipative case. With the derived expressions, we investigate the decay of solitary waves of the Korteweg-de Vries equation, when different kinds of dissipation are added.",
    keywords = "METIS-140893, IR-30253",
    author = "G.L.A. Derks and G. Derks and {van Groesen}, {Embrecht W.C.}",
    year = "1992",
    doi = "10.1016/0165-2125(92)90016-U",
    language = "Undefined",
    volume = "0",
    pages = "159--172",
    journal = "Wave motion",
    issn = "0165-2125",
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    }

    Energy propagation in dissipative systems Part II: Centrovelocity for nonlinear wave equations. / Derks, G.L.A.; Derks, G.; van Groesen, Embrecht W.C.

    In: Wave motion, Vol. 0, No. 15, 1992, p. 159-172.

    Research output: Contribution to journalArticleAcademicpeer-review

    TY - JOUR

    T1 - Energy propagation in dissipative systems Part II: Centrovelocity for nonlinear wave equations

    AU - Derks, G.L.A.

    AU - Derks, G.

    AU - van Groesen, Embrecht W.C.

    PY - 1992

    Y1 - 1992

    N2 - We consider nonlinear wave equations, first order in time, of a specific form. In the absence of dissipation, these equations are given by a Poisson system, with a Hamiltonian that is the integral of some density. The functional I, defined to be the integral of the square of the waveform, is a constant of motion of the unperturbed system. It will be shown that Z, the center of gravity of this density, is canonically conjugate to I and can be used as a measure to locate the position of the waveform. By introducing new coordinates based on Z, we get expressions for the centrovelocity, Image, and the decay of I, which compare to the ones of part I, in both the conservative and the dissipative case. With the derived expressions, we investigate the decay of solitary waves of the Korteweg-de Vries equation, when different kinds of dissipation are added.

    AB - We consider nonlinear wave equations, first order in time, of a specific form. In the absence of dissipation, these equations are given by a Poisson system, with a Hamiltonian that is the integral of some density. The functional I, defined to be the integral of the square of the waveform, is a constant of motion of the unperturbed system. It will be shown that Z, the center of gravity of this density, is canonically conjugate to I and can be used as a measure to locate the position of the waveform. By introducing new coordinates based on Z, we get expressions for the centrovelocity, Image, and the decay of I, which compare to the ones of part I, in both the conservative and the dissipative case. With the derived expressions, we investigate the decay of solitary waves of the Korteweg-de Vries equation, when different kinds of dissipation are added.

    KW - METIS-140893

    KW - IR-30253

    U2 - 10.1016/0165-2125(92)90016-U

    DO - 10.1016/0165-2125(92)90016-U

    M3 - Article

    VL - 0

    SP - 159

    EP - 172

    JO - Wave motion

    JF - Wave motion

    SN - 0165-2125

    IS - 15

    ER -