On the Collapse of Solutions of the Cauchy Problem for the Cubic Schrödinger Evolution Equation

It is proved that, for some initial data, the solutions of the Cauchy problem for the cubic Schrödinger evolution equation blow up in finite time whose exact value is estimated from above. In addition, lower bounds for the blow-up rate of the solution in certain norms are obtained.

     

Mixed problem for a cubic Schrödinger evolution equation with a cubic dissipative term

The question of the global solvability of a mixed problem for a Schrödinger evolution equation with a cubic dissipative term is considered.     

A2B6 electric-discharge semiconductor focon laser

The working principle of the electric-discharge semiconductor focon laser is considered. CdS, Cd _x Zn_1?x Se, and CdS _x Se_1?x plates were used as active medium. In the case of CdS, lasing at λ = 525 nm was observed. The radiation power reached 3 kW, the pulse duration being 3 ns. The conditions of generation initiation in the streamer regime are considered. The spectral characteristics of discharge channel radiation in Cd _x Zn_1?x Se and CdS _x Se_1?x plates are investigated. The spectrum is shown to consist of discrete lines occurring upon discharge propagation and corresponding to the change in the composition of the ternary compound obtained in the course of single crystal growth. The application of ternary solid solutions A2B6 is supposed to help in obtaining a successive laser pulse generation within the range of 480 to 700 nm.     

Nonlinear change in refractive index of Co2+:ZnSe at short-pulse single-beam 1.54-μm Z-scan probing

An experimental study and theoretical modeling of the nonlinear change in refractive index of a Co^{2 +}: ZnSe crystal at the short-pulse single-beam probing at the wavelength 1.54 μm is reported. In the experimental conditions of negligible contributions in the index non-linearity stemming from the Kerr-effect and inhomogeneous heating, the nonlinear change in refractive index in Co^{2 +}:ZnSe is shown to be caused by the resonant Co^{2 +} population-perturbation effect (i.e., by the Co^{2 +} ground-state absorption saturation). The Z-scan single-beam technique and novel theoretical approach addressing the resonant nonlinear refraction in a saturable doped medium are used, respectively, for an experimental and theoretical inspection of the phenomenon. For a set of Co^{2 +}:ZnSe samples with different concentrations of Co^{2 +} ions at the short-pulse (200 ns) mJ-range probing, we show that the maximal nonlinear change in refractive index is about of units of 10^{− 4} at the chosen wavelength.     

Absolute configuration of diastereomeric derivatives of N-substituted aziridine-2-carboxylic acids

Individual diastereomers of a number of anilides of N-substituted aziridine-2-carboxylic acids have been obtained. Conclusions regarding the spatial structure of the compounds indicated have been drawn on the basis of the ¹H NMR, ¹⁵N NMR, and CD spectra.Report 37 of the series entitled Asymmetric nonbridging nitrogen. For report 36 see [1].Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 10, pp. 1343–1348, October, 1984.