On the superstrong wave collapse

The development of wave collapse (WC) results in many cases in the formation of a long-living hot spot that draws continuously waves from the surrounding space. This important and widespread mechanism of nonlinear dissipation of wave energy in strong-turbulent processes has been lately studied intensively in the model of nonlinear Schroedinger equation (NLS) that describes the various types of WC in the d-dimensional space for sufficiently intensive initial conditions. For 4 ≤ sd < 2s+2 the short-living collapses (strong collapse with fixed energy trapped into singularity at sd=4 and weak collapse with continuously decreasing energy at sd > 4) take place. However, for sd ≥ 2s+2, a small-size dissipative zone (hot spot or black hole), which absorbs quasisteadily energy, is formed as a result of a weak collapse. This effect of long collapse, named as a superstrong wave collapse (SWC) is critically important for understanding of many macroscopic displays of strong wave turbulence (optical, plasma, and others). The SWC can be developed in the four different regimes. Note that the SWC phenomena may exist in the NLS independently of s at d>2. This means that the convenient and widely used model of forced damped NLS for studies of strong (collapsing) wave turbulence in nonlinear media can not take into account this significant effect for d≤2. Since long 3D computations of turbulence with multiple collapses are extremely expensive, there is an important problem of crating of the SWC models in lower dimensions