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In this study we examine the energy transfer mechanism during the nonlinearstage of the Modulational Instability (MI) in the modified Korteweg-de Vriesequation. The particularity of this study consists in considering the problemessentially in the Fourier space. A dynamical energy cascade model of thisprocess originally proposed for the focusing NLS-type equations is transposedto the mKdV setting using the existing connections between the KdV-type andNLS-type equations. The main predictions of the D-cascade model are outlinedand thoroughly discussed. Finally, the obtained theoretical results arevalidated by direct numerical simulations of the mKdV equation using thepseudo-spectral methods. A general good agreement is reported in this study.The nonlinear stages of the MI evolution are also investigated for the mKdVequation.

Direct dynamical energy cascade in the modified KdV equation