  In this Letter we demonstrate for the first time the formation of the inverse
energy cascade in the focusing modified Korteweg-de Vries (mKdV) equation. We
study numerically the properties of this cascade such as the dependence of the
spectrum shape on the initial excitation parameter (amplitude), perturbation
magnitude and the size of the spectral domain. Most importantly we found that
the inverse cascade is always accompanied by the direct one and they both form
a very stable quasi-stationary structure in the Fourier space in the spirit of
the FPU-like reoccurrence phenomenon. The formation of this structure is
intrinsically related to the development of the nonlinear stage of the
Modulational Instability (MI). These results can be used in several fields such
as the internal gravity water waves, ion-acoustic waves in plasmas and others.
