Direct dynamical energy cascade in water wave models

9780521763608The paper “Direct dynamical energy cascade in the modified KdV equation“, co-authored by Denys Dutykh and Elena Tobisch (nee Kartaschova),  has been published as a preprint on HAL. The paper examines the energy transfer mechanism during the nonlinear stage of the Modulational Instability (MI) in the modified Korteweg-de Vries equation. The particularity of this study consists in considering the problem essentially in Fourier space. A dynamical energy cascade model of this process originally proposed for the focusing NLS-type equations is transposed to the mKdV setting using the existing connections between the KdV-type and NLS-type equations. The main predictions of the D-cascade model are outlined and thoroughly discussed. Finally, the obtained theoretical results are validated by direct numerical simulations of the mKdV equation using pseudo-spectral methods.  Good agreement with the theory is reported in this study.  This paper is a followup to the published paper “Observation of the inverse energy cascade in the modified KdV equation“, by Denys Dutykh and Elena Tobisch, which was published in Europhysics Letters in June 2014.  A link to the published paper is here.

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