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78) at ψ0 = 0 [23, 21]. 7 Anisotropic black holes As we saw in the previous section the black hole regime becomes quasiclassical starting from D = 4. In this section we want to present an example showing how, due to the medium anisotropy, the “eﬀective dimension D can be greater than 4 and, as a consequence, the black-hole regime can be realized. 84) where ωce , ωpe are electron gyrofrequency and electron plasma frequency, respectively, rd = vT e / ωpe is the Debye radius, k⊥ is the component transverse to the external magnetic ﬁeld B 0 , directed along the z axis.

68) What is the scenario of the collapse? 70) g(∞) = 0. 70). 71) hence |ψ|2 → 1/r2 as t → t0 . 71) is integrable. 69) describes collapse in a general position. So far, the only way to check this conjecture is by a numerical experiment. Two series of experiments performed by two independent groups conﬁrmed the hypothesis with a very high accuracy [20, 23]. This problem was also discussed in many other papers. We would like to draw attention to some of them - [74] and [30]. A. E. Zakharov A generic case D > 2 can be called supercritical.

Consequently, their nonlinear interaction will be negligible with respect to their dispersion and they will have a positive Hamiltonian. Therefore due to the wave radiation, the Hamiltonian of the region HΩ will become more and more negative increasing its absolute value, that is possible only due to the unboundedness of the Hamiltonian. s. 63) will increase. It automatically leads to the growth of the maximal value of |ψ|2 . Thus, radiation, as a dissipative process promotes the wave collapse.