  We consider developed turbulence in the 2D Gross-Pitaevsky model, which
describes wide classes of phenomena from atomic and optical physics to
condensed matter, fluids and plasma. The well-known difficulty of the problem
is that the hypothetical local spectra of both inverse and direct cascades in
the weak-turbulence approximation carry fluxes which are either zero or have
the wrong sign; such spectra cannot be realized. We analytically derive the
exact flux constancy laws (analogs of Kolmogorov's 4/5-law for incompressible
fluid turbulence), expressed via the fourth-order moment and valid for any
nonlinearity. We confirm the flux laws in direct numerical simulations. We show
that a constant flux is realized by non-local wave interaction in both the
direct and inverse cascades. Wave spectra (second-order moments) are close to
slightly (logarithmically) distorted thermal equilibrium in both cascades.
