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    Periodic Traveling Waves of the Regularized Short Pulse and Ostrovsky Equations: Existence and Stability

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    Issue Date
    2017
    Author
    Hakkaev, Sevdzhan
    Stanislavova, Milena
    Stefanov, Atanas G.
    Publisher
    Society for Industrial and Applied Mathematics
    Type
    Article
    Article Version
    Scholarly/refereed, publisher version
    Rights
    © 2017, Society for Industrial and Applied Mathematics
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    Abstract
    We construct various periodic traveling wave solutions of the Ostrovsky/Hunter--Saxton/short pulse equation and its KdV regularized version. For the regularized short pulse model with small Coriolis parameter, we describe a family of periodic traveling waves which are a perturbation of appropriate KdV solitary waves. We show that these waves are spectrally stable. For the short pulse model, we construct a family of traveling peakons with corner crests. We show that the peakons are spectrally stable as well.
    URI
    http://hdl.handle.net/1808/27523
    DOI
    https://doi.org/10.1137/15M1037901
    Collections
    • Mathematics Scholarly Works [282]
    Citation
    Hakkaev, S., Stanislavova, M., & Stefanov, A. (2017). Periodic traveling waves of the regularized short pulse and Ostrovsky equations: existence and stability. SIAM Journal on Mathematical Analysis, 49(1), 674-698.

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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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