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    Determining form and data assimilation algorithm for weakly damped and driven Korteweg-de Vries equation - Fourier modes case

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    Determining Form and Data Assimilation_Final.pdf (504.2Kb)
    Date
    2017-08
    Author
    Jolly, Michael S.
    Sadigov, Tural
    Titi, Edriss S.
    Publisher
    Nonlinear Analysis: Real World Applications
    Metadata
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    Subject
    KdV equation
    data assimilation
    Korteweg–de Vries equation
    differential equations
    determining form
    Fourier mode
    Abstract
    We show that the global attractor of a weakly damped and driven Korteweg–de Vries equation (KdV) is embedded in the long-time dynamics of an ordinary differential equation called a determining form. In particular, there is a one-to-one identification of the trajectories in the global attractor of the damped and driven KdV and the steady state solutions of the determining form. Moreover, we analyze a data assimilation algorithm (down-scaling) for the weakly damped and driven KdV. We show that given a certain number of low Fourier modes of a reference solution of the KdV equation, the algorithm recovers the full reference solution at an exponential rate in time.
    URI
    http://hdl.handle.net/1951/69167
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    • SUNY Polytechnic Institute Faculty and Staff Research, Publications, and Creative Works [63]

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