We study the semi-classical limit of the nonlinear Schrödinger-Poisson (NLSP) equation for initial data of the WKB type. The semi-classical limit in this case is realized in terms of a density-velocity pair governed by the Euler-Poisson equations. Recently we have shown in [ELT, Indiana Univ. Math. J., 50 (2001), 109–157], that the isotropic Euler-Poisson equations admit a critical threshold ph...

We consider the Helmholtz equation in the half space and suggest two methods for determining the boundary impedance from knowledge of the far field pattern of the time-harmonic incident wave. We introduce a potential for which the far field patterns in specially selected directions represent its Fourier coefficients. The boundary impedance is then calculated from the potential by an explicit fo...

Behavioral states alternate between wakefulness (wk), rapid eye movement (rem) and non-rem (nrem) sleep at time scale of hours i.e., light and dark cycle rhythms and from several tens of minutes to seconds (i.e., brief awakenings during sleep). Using statistical analysis of bout duration, Markov chains of sleep-wk dynamics and quantitative EEG analysis, we evaluated the influence of light/dark ...

The Wentzel-Kramers-Brillouin (WKB) perturbative series, a widely used technique for solving linear waves, is typically divergent and, at best, asymptotic, thus impeding predictions beyond the first few leading-order effects. Here, we report closed-form formula that exactly resums WKB series to all orders two turning point problems. elegantly interpreted as action evaluated using product of spa...