Clipping -- a new investigation method for PDEs in compact domains (Q1918839)

We consider a class of nonlinear evolution equations with dispersive linear part and nonlinear part small enough in the sense that the nonlinear effects are weak. We hold also that these equations admit the resonant interactions. The present paper is devoted to a detailed study of the partitioning of the resonantly interacting waves into small groups. We demonstrate that this feature gives us the powerful tool to study the energy transfer via the spectrum governed by some specific partial differential equations for a wide class of initial conditions. In Section 2 the value of frequency disbalance is estimated for which the partition still conserves. The method which allows us to clip out the most part of the spectral modes and use only a few modes to describe the wavefield evolution governed by specific partial differential equations -- the clipping method -- is described in Section 3. The results of the clipping method application to the barotropic vorticity equation are represented in Section 4. We briefly discuss the obtained results in Section 5.