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    Stability of Periodic Traveling Waves for Nonlinear Dispersive Equations

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    JohnsonMathew_2015.pdf (308.2Kb)
    Issue Date
    2015-09-17
    Author
    Hur, Vera Mikyoung
    Johnson, Mathew A.
    Publisher
    Society for Industrial and Applied Mathematics
    Type
    Article
    Article Version
    Scholarly/refereed, publisher version
    Rights
    © 2015, Society for Industrial and Applied Mathematics
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    Abstract
    We study the stability and instability of periodic traveling waves for Korteweg--de Vries-type equations with fractional dispersion and related, nonlinear dispersive equations. We show that a local constrained minimizer for a suitable variational problem is nonlinearly stable to period preserving perturbations, provided that the associated linearized operator enjoys a Jordan block structure. We then discuss when the linearized equation admits solutions exponentially growing in time.
    URI
    http://hdl.handle.net/1808/22140
    DOI
    https://doi.org/10.1137/12090215X
    Collections
    • Mathematics Scholarly Works [283]
    Citation
    Hur, V. M., & Johnson, M. A. (2015). Stability of periodic traveling waves for nonlinear dispersive equations. SIAM Journal on Mathematical Analysis, 47(5), 3528-3554.

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    Contact KU ScholarWorks
    785-864-8983
    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    785-864-8983

    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    Image Credits
     

     

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