The effect of fiber loss, amplification, and sliding-frequency filters on the evolution of optical pulses in nonlinear optical fibers is considered, this evolution being governed by a perturbed nonlinear Schrödinger (NLS) equation. Approximate ordinary differential equations (ODE's) governing the pulse evolution are obtained using conservation and moment equations for the perturbed NLS equation...

Using symmetry analysis we systematically present a higher-dimensional similarity transformation reducing the (3+1) -dimensional inhomogeneous nonlinear Schrödinger (NLS) equation with variable coefficients and parabolic potential to the (1+1) -dimensional NLS equation with constant coefficients. This transformation allows us to relate certain class of localized exact solutions of the (3+1) -di...

We consider periodic traveling wave solutions to the focusing nonlinear Schrödinger equation (NLS) that have been shown to persist when the NLS is perturbed to the complex Ginzburg-Landau equation (CGL). In particular, we show that these periodic traveling waves are spectrally stable solutions of NLS with respect to periodic perturbations. Furthermore, we use an argument based on the Fredholm a...

In this work we want to describe a discrete version of the well–known Adomian decomposition method (ADM) applied to the discrete nonlinear Schrödinger equation (NLS). The ADM was introduced by Adomian [3], [11] in the early 1980s to solve nonlinear ordinary and partial differential equations. The discrete nonlinear Schrödinger equation is omnipresent [8] in applied sciences, e.g. describing the...

The critical nonlinear SchrSdinger equation (NLS) models the propagation of intense laser light ill Kerr media. This equation is derived from tile more conq)reheasive nonlinear Hehnholtz e(tuation (NLH) t)y employing the paraxial at)t)roximation and negle(:ting th(' backscattered waves. It is known that if the input power of tile laser beam (i.e., L2 norm of the ilfitial soh,ti(m) is sufficient...

The initial-value problem for the focusing nonlinear Schrödinger (NLS) equation is solved numerically by following the various steps of the inverse scattering transform. Starting from the initial value of the solution, a Volterra integral equation is solved followed by three FFT to arrive at the reflection coefficient and initial Marchenko kernel. By convolution these initial data are propagate...

Nonlinear evolution equations are of tremendous interest in both theory and applications. In this talk we introduce parallel algorithms for numerical simulations of CMKdV, NLS and and CNLS equations in 1+1 and 1+2 dimensions. The parallel methods are implemented on multiprocessor system. Numerical experiments have shown that these methods give accurate results and considerable speedup. This tal...

We present a model of optical communication system for high-bitrate data transmission in the nonreturn-to-zero (NRZ) format over transoceanic distance. The system operates in a small group velocity dispersion regime, and the model equation is given by the Whitham equations describing the slow modulation of multi-phase wavetrains of the (defocusing) nonlinear Schrödinger (NLS) equation. The mode...

We study theoretically, numerically and experimentally the nonlinear propagation of partially incoherent optical waves in single mode optical fibers. We revisit the traditional treatment of the wave turbulence theory to provide a statistical kinetic description of the integrable scalar NLS equation. In spite of the formal reversibility and of the integrability of the NLS equation, the weakly no...

A nonlinear Schrödinger NLS equation with an effect of viscosity is derived from a Kortewegde Vries KdV equation modified with viscosity using the method of multiple time scale. It is well known that the plane-wave solution of the NLS equation exhibits modulational instability phenomenon. In this paper, the modulational instability of the plane-wave solution of the NLS equation modified with vi...