Ultra-short pulse is a promising technology for achieving ultra-high data rate transmission which is required to follow the increased demand of data transport over an optical communication system. Therefore, the propagation of such type of pulses and the effects that it may suffer during its transmission through an optical waveguide has received a great deal of attention in the recent years. We...

Frozen orbits of the Hill problem are determined in the double-averaged problem, where short and long-period terms are removed by means of Lie transforms. Due to the perturbation method we use, the initial conditions of corresponding quasi-periodic solutions in the nonaveraged problem are computed straightforwardly. Moreover, the method provides the explicit equations of the transformation that...

The existence of quasi-periodic eigensolutions of a linear second order ordinary differential equation with quasi-periodic coefficient f{a>it, io%t) is investigated numerically and graphically. For sufficiently incommensurate frequencies coi, a>2 a doubly indexed infinite sequence of eigenvalues and eigenmodes is obtained. The equation considered is a model for the magneto-hydrodvnamic "continu...

In this paper, we define random quasi-periodic paths for dynamical systems and measures Markovian semigroups. We give a sufficient condition the existence uniqueness of stochastic differential equations density measure to exist satisfy Fokker-Planck equation. obtain an invariant by considering lifted flow semigroup on cylinder tightness average measures. further prove that is unique, thus ergod...