Nonlinear Optics has continued to develop over the last few years at an extremely fast pace, with significant advances being reported in nonlinear optical metamaterials, optical signal processing, quantum optics, nonlinear optics at subwavelength scale, and biophotonics. These exciting new developments have generated significant potential for a broad spectrum of technological applications in wh...

Singular spectrum analysis (SSA), a linear univariate and multivariate time series technique , is essentially principal component analysis (PCA) applied to the time series and additional copies of the time series lagged by 1 to K time steps. Neural network theory has meanwhile allowed PCA to be generalized to nonlinear PCA (NLPCA). In this paper, NLPCA is further extended to perform nonlinear S...

We study the modulational instability in surface gravity waves with random phase spectra. Starting from the nonlinear Schrödinger equation and using the Wigner-Moyal transform, we study the stability of the narrow-banded approximation of a typical wind-wave spectrum, i.e., the JONSWAP spectrum. By performing numerical simulations of the nonlinear Schrödinger equation we show that in the unstabl...

Background and Aims: Biomolecules' optical and nonlinear optical properties are widely used for different medical diagnoses and applications in biophotonic devices. These properties are essential in studying biological processes in living tissues. Aside from biomolecules' linear optical characteristics, their nonlinear optical characteristics have lately been considered. Materials and Methods:...

It is shown that the nonlinear mapping relation between a surface gravity wave spectrum and its SAR image spectrum, as derived by Hasselmann and Hasselmann [1], is not complete. The reason for this is that the velocity bunching effect is so nonlinear that effects of skewness and kurtosis are as important as the nonlinear terms already retained in the Hasselmann and Hasselmann approach. An analy...

The standard linear technique of impulse response function analysis is extended to the nonlinear case by de"ning a generalized impulse response function. Measures of persistence and asymmetry in response are constructed for a wide class of time series. ( 2000 Elsevier Science B.V. All rights reserved. JEL classixcation: C22; C51; C52; E32

An important group of nonlinear processes in optical fibre involves the mixing of four waves due to the intensity dependence of the refractive index. It is customary to distinguish between nonlinear effects that require external/pumping waves (cross-phase modulation and parametric processes such as four-wave mixing) and self-action of the propagating optical field (self-phase modulation and mod...

This paper aims at investigating the nonlinear behavior of a system which is consisting of two free-free beams which are connected by a nonlinear joint. The nonlinear system is modelled as an in-extensional beam with Timoshenko beam theory. In addition, large amplitude vibration assumption is taken into account in order to obtain exact results. The nonlinear assumption in the system necessities...