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

G. Derks, E. van Groesen

    Research output: Contribution to journalArticleAcademicpeer-review

    6 Citations (Scopus)
    55 Downloads (Pure)

    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 languageEnglish
    Pages (from-to)159-172
    Number of pages14
    JournalWave motion
    Volume15
    Issue number2
    DOIs
    Publication statusPublished - 1992

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