  In this work, we discuss a situation which could lead to both wave turbulence
and collective behavior kinetic equations. The wave turbulence kinetic models
appear in the kinetic limit when the wave equations have local differential
operators. Viewing wave equations on the lattice as chains of anharmonic
oscillators and replacing the local differential operators (short-range
interactions) by non-local ones (long-range interactions), we arrive at a new
Vlasov-type kinetic model in the mean field limit under the molecular chaos
assumption reminiscent of models for collective behavior in which anharmonic
oscillators replace individual particles.
