  The kinetic wave equation arises in wave turbulence to describe the Fourier
spectrum of solutions to the cubic Schroedinger equation. The equation has two
Kolmogorov-Zakharov steady states corresponding to out-of-equilibrium cascades
transferring for the first solution mass from infinity to zero (small spatial
scales to large scales) and for the other solution energy from zero to
infinity. After conjecturing the generic development of the two cascades, we
verify it partially in the isotropic case by proving the nonlinear stability of
the mass cascade in the stationary setting. This constructs non-trivial
out-of-equilibrium steady states with a direct energy cascade as well as an
indirect mass cascade.
