Nonlinear Science at the Dawn of the 21st Century by E.A. Kuznetsov, V.E. Zakharov (auth.), P. L. Christiansen,

By E.A. Kuznetsov, V.E. Zakharov (auth.), P. L. Christiansen, M. P. Sørensen, A. C. Scott (eds.)

Nonlinear technological know-how is through now a good verified box of analysis on the interface of many conventional disciplines and attracts at the theoretical ideas built in physics and arithmetic. the current quantity gathers the contributions of prime scientists to offer the state-of-the-art in lots of components strongly stimulated by means of nonlinear study, akin to superconduction, optics, lattice dynamics, biology and biomolecular dynamics. whereas this quantity is essentially meant for researchers operating within the box care, has been taken that it'll even be of profit to graduate scholars or nonexpert scientist wishing to familiarize themselves with the present prestige of research.

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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.

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