Kinetic equation and Clipping - two limits of wave turbulence theory”. E-print arXiv.org:math-ph/0509006

Different dynamics, described by kinetic equation and clipping method is shown as well as a role of approximate resonances in wave turbulence theory. Applications of clipping method are sketched for gravity-capillary and drift waves. Brief discussion of possible transition from continuous spectrum (= kinetic equation) to discrete spectrum (= clipping) is given at the end. 1 Introductory remarks Wave kinetic equation has been developed in 60-th (see, for instance, [7], [11]) and applied for many different types evolution PDEs. Kinetic equation is approximately equivalent to the initial nonlinear PDE but has more simple form allowing direct numerical computations of each wave amplitudes in a given domain of wave spectrum. Wave kinetic equation is an averaged equation imposed on a certain set of correlation functions and it is in fact one limiting case of the quantum BoseEinstein equation while the Boltzman kinetic equation is its other limit. Some statistical assumptions have been used in order to obtain kinetic equations and limit of its applicability then is a very complicated problem which should be solved separately for each specific ∗Author acknowledges support of the Austrian Science Foundation (FWF) under projects SFB F013/F1304.