  In this paper we give a general account of Wave Interaction Theory which by
now consists of two parts: kinetic wave turbulence theory (WTT), using a
statistical description of wave interactions, and the D-model recently
introduced in \emph{Kartashova, PRE \textbf{86}: 041129 (2012)} describing
interactions of distinct modes. Applying time scale analysis to weakly
nonlinear wave systems modeled by the focusing nonlinear Sch\"{o}dinger
equation, we give an overview of the structures appearing in Wave Interaction
Theory, their time scales and characteristic times. We demonstrate that kinetic
cascade and D-cascade are not competing processes but rather two processes
taking place at different time scales, at different characteristic levels of
nonlinearity and due to different physical mechanisms. Taking surface water
waves as an example we show that energy cascades in this system occur at much
faster characteristic times than those required by the kinetic WTT but can be
described as D-cascades. As D-model has no special pre-requisites, it may be
rewarding to re-evaluate existing experiments in other wave systems appearing
in hydrodynamics, nonlinear optics, electrodynamics, plasma, convection theory,
etc.
  To appear in EPL
