Showing papers by "University of Madeira published in 1994"

Direct perturbation theory for dark solitons

Abstract: Perturbation theory for dark solitons governed by the nonlinear Schr\"odinger equation is developed. Orthogonality and closure of the basis of squared Jost functions are proved. The general form of a correction to the one-soliton solution up to first order is obtained. Two examples related to perturbed dynamics of dark optical solitons are considered within the framework of the adiabatic approximation.

A self-consistent analytical model of arc spots on electrodes

Abstract: A simple model of quasi-stationary electrode spots in arc discharges is presented. For a given dependence of parameters of the near-electrode plasma layer on the local surface temperature and on the voltage drop in the layer, the model allows one to evaluate integral parameters of the spots without using empirical parameters such as the value of the electric current per spot or arbitrary suppositions such as the principle of minimum voltage. Analytical formulas are obtained for the spot radius, integral heat flux removed by heat conduction, and the electric current per spot. >

An Introduction to White Noise Analysis

Abstract: The Gaussian white noise measure μ (on the Borel algebra over cylinder sets of real, tempered distributions ω ∈ S * (R d )) is conveniently described by its characteristic function: $$C(f) = E({e^{i }}) = \int\limits_{S*} {d\mu [\omega ]{e^{i }}} = {e^{ - \tfrac{1}{2}\int {{f^{2(t)dt}}} }},f \in S({R^d})$$ (1.1)