The development of modulation instability for two beams copropagating in a medium with noninstantaneous nonlinear response is investigated. The frequency dependence of the experimentally observed spectral broadening reveals the presence of two-beam coupling, resulting from the time-delayed Raman part of the third-order nonlinear susceptibility. We present an analysis of the experimental data, w...

Estimation of the state levels of a discrete-time, finite-state Markov chain hidden in coloured Gaussian noise and subjected to unknown nonlinear distortion is considered. If the nonlinear distortion has almost linear behaviour for small values near zero or for large values, extreme value theory can be applied to the level estimation problem, resulting in simple estimation algorithms. The extre...

The linear structural model has provided the statistical backbone of the analysis of twin and family data for 25 years. A new generation of questions cannot easily be forced into the framework of current approaches to modeling and data analysis because they involve nonlinear processes. Maximizing the likelihood with respect to parameters of such nonlinear models is often cumbersome and does not...

sinc-galerkin method based upon double exponential transformation for solving troesch's problem was given in this study. properties of the sinc-galerkin approach were utilized to reduce the solution of nonlinear two-point boundary value problem to same nonlinear algebraic equations, also, the matrix form of the nonlinear algebraic equations was obtained.the error bound of the method was fo...

In this work, we establish sufficient conditions for the existence of solutions for a three point boundary value problem generated by a third order differential equation. We give sufficient conditions that allow us to obtain the existence of a nontrivial solution. Then by using the Leray Schauder nonlinear alternative we prove the existence of at least one solution of the posed problem. As an a...

In this paper we study nonlinear second-order differential inclusions involving the ordinary vector p-Laplacian, a multivalued maximal monotone operator and nonlinear multivalued boundary conditions. Our framework is general and unifying and incorporates gradient systems, evolutionary variational inequalities and the classical boundary value problems, namely the Dirichlet, the Neumann and the p...

An impulsive boundary value problem with nonlinear boundary conditions for a second order ordinary differential equation is studied. In particular, sufficient conditions are provided so that a compression expansion cone theoretic fixed point theorem can be applied to imply the existence of positive solutions. The nonlinear forcing term is assumed to satisfy usual sublinear or superlinear growth...

Consider a bounded domain G C R (_N>1) with smooth boundary T . Let L be a uniformly elliptic linear differential operator. Let y and ß be two maximal monotone mappings in R. We prove that, when y ? 2 satisfies a certain growth condition, given f £ L (G ) there is u € H (G) such that Lu + y(u) 3 f a.e. on G, and -du/d v e ß(u\ ) a.e. on T, where du/civ is the conormal derivative associated with...