Decay of travelling waves in dissipative Poisson systems

E. van Groesen, F.P.H. van Beckum, T.P. Valkering

    Research output: Contribution to journalArticleAcademicpeer-review

    6 Citations (Scopus)
    79 Downloads (Pure)

    Abstract

    In many finite and infinite dimensional systemslow-dimensional behaviour is often observed. That is to say, the dynamics, observed experimentally or numerically, looks as if it can be described (approximately) with only a few essential parameters. Choosing the correct set of such ldquorobust observablesrdquo is an essential ingredient of a successful low dimensional description. This paper reports on a specific example of a more general approach that aims at describing certain (low dimensional) phenomena in (high dimensional) damped/driven equations with parameters that are essentially determined from the underlying conservative part of the equation. In particular, a Hamiltonian or a Poisson structure of the conservative part is exploited to find (characterize) families of exact solutions. These solutions are then used as the ldquobase functionsrdquo with the aid of which the solutions of the disturbed system are approximated. This approximation is accomplished using the parameters that characterize the family as variables that depend on time. In this paper, this procedure is applied to a class of systems which admit travelling waves when dissipation is ignored.
    Original languageEnglish
    Pages (from-to)501-523
    Number of pages24
    JournalZeitschrift für angewandte Mathematik und Physik
    Volume41
    Issue number4
    DOIs
    Publication statusPublished - 1990

    Keywords

    • Exact solution
    • Base function
    • Mathematical method
    • Poisson structure
    • Essential ingredient

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