  We performed numerical simulations of decaying quantum turbulence by using a
generalized Gross-Pitaevskii equation, that includes a beyond mean field
correction and a nonlocal interaction potential. The nonlocal potential is
chosen in order to mimic He II by introducing a roton minimum in the excitation
spectrum. We observe that at large scales the statistical behavior of the flow
is independent of the interaction potential, but at scales smaller than the
intervortex distance a Kelvin wave cascade is enhanced in the generalized
model. In this range, the incompressible kinetic energy spectrum obeys the weak
wave turbulence prediction for Kelvin wave cascade not only for the scaling
with wave numbers but also for the energy fluxes and the intervortex distance.
