Table of contents

The general properties of a class of nonlinear Schroedinger equations: iu_t + p:∇∇u + f(|u|²)u = 0 are reviewed. Conditions for existence, uniqueness, and stability of solitary wave solutions are presented, along with conditions for blow-up and global existence for the Cauchy problem.

A critical review of the literature on similarity solutions of nonlinear Schroedinger equations is presented. We demonstrate that the self-similar blow-up solutions discovered hitherto are all associated either with a simple stretching invariance, or with a slightly more complicated conformal invariance and generalizations of the latter. This generalized "quasi-invariance" reveals the nature of the blow-up singularity and resolves an old controversy. Most of the previous work has been done on the cubic nonlinearity. We generalize the results to an arbitrary power nonlinearity.

We reduce N = 1 supersymmetric Yang-Mills theory from D = 4, N = 1 superspace to D = 4, N = 1/2 superspace and solve the field strength constraints in terms of a N = 1/2 prepotential. The natural N = 1/2 gauge choice reduces the gauge freedom to that of the x-space components and the potential enters linearly rather than exponentially in the covariant derivative. We present the manifest as well as the explicit part of the supersymmetry transformations.

Spectra from laserproduced plasmas of scandium, vanadium, chromium and manganese have been recorded in the region 200-600 Å. All the principal lines of the 3s-3p and 3p-3d transition arrays in the neonlike ions of these elements have been identified. Isoelectronic regularities of the wavenumbers have been studied, and the observations are compared with predictions from Dirac-Fock calculations.

We report on lifetime measurements in Ta II using a pulsed low pressure hollow-cathode discharge as an ion source. Pulsed laser excitation and time-resolved detection were employed.

The nonlinear development of the E × B-instability in a weakly ionized plasma is governed by an infinite set of coupled ordinary nonlinear differential equations for the amplitudes of the modes of the system. The solution of these equations are investigated in the adiabatic approximation by setting the time derivative of linearly stable modes equal to zero. Approximate analytical solutions for the time development of the different modes, in good agreement with previous numerical results, have been obtained for control parameters fifteen times the critical value. The results clearly indicate the possible existence of a cascading process, where the amplitudes of the linearly most stable modes have the highest nonlinear growth rates.

A statistical model for soliton-particle interaction is presented. A master equation is derived for the time evolution of the particle velocity distribution as induced by resonant interaction with Korteweg-de Vries solitons. The detailed energy balance during the interaction subsequently determines the evolution of the soliton amplitude distribution. The analysis applies equally well for weakly nonlinear plasma waves in a strongly magnetized waveguide, or for ion acoustic waves propagating in one-dimensional systems.

Specific features of the Rayleigh Scattering of Mössbauer Radiation (RSMR) technique in the study of biological systems are described. Experimental data show that the temperature and hydration degree are the principal parameters which influence intramolecular mobility in biopolymers. Data on temperature dependencies of elastic fraction, f, and spectrum line-shape do not fit neither Debye or Einstein models of solids nor the free diffusion in liquids and demand for their explanation a multimode approximation (i.e. a wide spectrum of correlation times, at T = 293 K from 10^-6 s to 10^-12-10^-13 s). On the basis of RSMR, low temperature specific heat and X-ray dynamic analysis data and from the general conditions that information macromolecule must be in a non-equilibrium state (an independent confirmation of this fact comes from the kinetic model of protein folding) a glass-like dynamical model of biopolymers is formulated. A possible interpretation of RSMR data shows that fluctuatively prepared tunneling between quasiequilibrium positions (QEP) can prevail activated transitions up to a room temperature.