The soliton transform and a possible application to nonlinear Alfvén waves in space

T. Hada, R. L. Hamilton, C. F. Kennel

    Research output: Contribution to journalArticle

    13 Citations (Scopus)

    Abstract

    We apply the inverse scattering transform (IST) based upon the Derivative Nonlinear Schrödinger (DNLS) equation to a complex time series of nonlinear Alfvén wave data generated by numerical simulation. The IST describes the long‐time evolution of quasi‐parallel Alfvén waves more efficiently than the Fourier transform, which is adapted to linear, not nonlinear, problems. When we add dissipation, so the conditions for the validity of the DNLS are not strictly satisfied, the IST continues to provide a compact description of the wave‐field in terms of a small number of decaying envelope solitons. Since large amplitude Alfvén waves and other nonlinear waves play essential roles in various space environments—the solar wind is one obvious example—we suggest that it may be of interest to investigate how inverse scattering transforms can be developed into practical tools for the analysis of space data.

    Original languageEnglish
    Pages (from-to)779-782
    Number of pages4
    JournalGeophysical Research Letters
    Volume20
    Issue number9
    DOIs
    Publication statusPublished - May 7 1993

    Fingerprint

    nonlinear wave
    inverse scattering
    transform
    solitary waves
    scattering
    Fourier transform
    nonlinear equations
    solar wind
    dissipation
    envelopes
    time series
    simulation

    All Science Journal Classification (ASJC) codes

    • Geophysics
    • Earth and Planetary Sciences(all)

    Cite this

    The soliton transform and a possible application to nonlinear Alfvén waves in space. / Hada, T.; Hamilton, R. L.; Kennel, C. F.

    In: Geophysical Research Letters, Vol. 20, No. 9, 07.05.1993, p. 779-782.

    Research output: Contribution to journalArticle

    Hada, T. ; Hamilton, R. L. ; Kennel, C. F. / The soliton transform and a possible application to nonlinear Alfvén waves in space. In: Geophysical Research Letters. 1993 ; Vol. 20, No. 9. pp. 779-782.
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