We introduce the theory of modulational instability (MI) of electromagnetic waves in fibers with random polarization mode dispersion. Applying a linear stability analysis and stochastic calculus, we show that the MI gain spectrum reads as the maximal eigenvalue of a constant effective matrix. In the limiting cases of small or large fluctuations, we give explicit expressions for the MI gain spec...

We report on the theoretical and experimental study of the generation of propagating waveguide modes on the water surface. These propagating modes are modulated in the transverse direction in a manner that satisfies boundary conditions on the walls of the water tank. It is shown that the propagating modes possess both anomalous and normal dispersion regimes, in contrast to the extensively studi...

We survey recent advances in the analysis of the large data global (and asymptotic) behaviour of nonlinear dispersive equations such as the non-linear wave (NLW), nonlinear Schrödinger (NLS), wave maps (WM), Schrödinger maps (SM), generalised Korteweg-de Vries (gKdV), Maxwell-Klein-Gordon (MKG), and Yang-Mills (YM) equations. The classification of the nonlin-earity as subcritical (weaker than t...

This paper considers double generalized linear models, which allow the mean and dispersion to be modelled simultaneously in a generalized linear model context. Estimation of the dispersion parameters is based on a χ1 approximation to the unit deviances, and the accuracy of the saddle-point approximation which underlies this is discussed. Approximate REML methods are developed for estimation of ...

In this paper the guidelines for applying heteroscedastic linear models for analysing industrial process data is presented. Heteroscedastic linear models are considered as a good model family for the joint modelling of dispersion and mean. The model selection of heteroscedastic linear model is discussed considering the special features of industrial data. A procedure for dispersion model select...

AbstractIn this paper we will study the various method of dispersion compensation in single mode fiber created because of dependence of group index to wavelength known as chromatic dispersion. Various methods of dispersion compensation are Dispersion compensation fiber (DCF) which compensates dispersion at 1310nm and 1550 nm and Fiber Bragg gratings (FBG) which compensate dispersion at waveleng...