Features of the dynamics of nonlinear waves in plane domains

An analysis of the dynamics of three-dimensional nonlinear waves on a torus has shown that their attractors are the so-called self-organization regimes, which are created from trajectories crowding together and have several remarkable features. Specifically, they are well ordered with respect to spatial and time variables, and their energy is fairly high and decreases gradually with decreasing elasticity coefficient, which itself evolves into a diffusion chaos. The role of this paper is twofold. First, the features of self-organization regimes are analyzed in the case of Neumann boundary conditions. Second, the stages leading to the detection of this phenomenon are described in detail.