Related papers: Fast Numerical Nonlinear Fourier Transforms
We investigate integral formulations and fast algorithms for the steady-state radiative transfer equation with isotropic and anisotropic scattering. When the scattering term is a smooth convolution on the unit sphere, a model reduction step…
Two signal multiplexing schemes for optical fiber communication are considered: Wavelength-division multiplexing (WDM) and nonlinear frequency-division multiplexing (NFDM), based on the nonlinear Fourier transform (NFT). Achievable…
Spectral method related to Lame equation with finite-gap potential is used to study the optical cascading equations. These equations are known not to be integrable by inverse scattering method. Due to "partial integrability" two-gap…
We consider the numerical solution of the scattering of time-harmonic plane waves from an infinite periodic array of reflection or transmission obstacles in a homogeneous background medium, in two dimensions. Boundary integral formulations…
Despite being the most popular methods of data analysis, Fourier-based techniques suffer from the problem of static resolution that is currently believed to be a fundamental limitation of the Fourier Transform. Although alternative…
New services and applications are causing an exponential increase in internet traffic. In a few years, current fiber optic communication system infrastructure will not be able to meet this demand because fiber nonlinearity dramatically…
Machine learning applied to computer vision and signal processing is achieving results comparable to the human brain on specific tasks due to the great improvements brought by the deep neural networks (DNN). The majority of state-of-the-art…
Space time fractional nonlinear evolution equations have been widely applied for describing various types of physical mechanism of natural phenomena in mathematical physics and engineering. The proposed generalized exp expansion method…
A method of windowed spatio-temporal spectral filtering is proposed to segregate different nonlinear wave components, and to calculate the surface of free waves. The dynamic kurtosis (i.e., produced by the free wave component) is shown able…
Recent research in deep learning (DL) has investigated the use of the Fast Fourier Transform (FFT) to accelerate the computations involved in Convolutional Neural Networks (CNNs) by replacing spatial convolution with element-wise…
The coupled cubic nonlinear Schr\"odinger (CNLS) equations are used to study modulational instabilities of a pair of nonlinearly interacting two-dimensional waves in deep water. It has been shown that the full dynamics of these interacting…
Modified scattering phenomena are encountered in the study of global properties for nonlinear dispersive partial differential equations in situations where the decay of solutions at infinity is borderline and scattering fails just barely.…
We consider the modulational instability of nonlinearly interacting two-dimensional waves in deep water, which are described by a pair of two-dimensional coupled nonlinear Schroedinger equations. We derive a nonlinear dispersion relation.…
We propose an implementation of the quantum fast Fourier transform algorithm in an entangled system of multilevel atoms. The Fourier transform occurs naturally in the unitary time evolution of energy eigenstates and is used to define an…
We present an efficient, fast and robust Nonlinear Fourier Transform (NFT) algorithm to detect eigenvalues of the discrete spectrum. It outperforms other known NFT algorithms as it detects the eigenvalues from the continuous spectrum, the…
We consider the quintic nonlinear Schr\"odinger equation (NLS) on the circle. We prove that there exist solutions corresponding to an initial datum built on four Fourier modes which form a resonant set, which have a non trivial dynamic that…
The Fourier Transform is one of the most important linear transformations used in science and engineering. Cooley and Tukey's Fast Fourier Transform (FFT) from 1964 is a method for computing this transformation in time $O(n\log n)$.…
Suppression of wave scattering and the realization of transparency effects in engineered optical media and surfaces have attracted great attention in the past recent years. In this work the problem of transparency is considered for optical…
This article addresses the problem of two- and higher dimensional pattern matching, i.e. the identification of instances of a template within a larger signal space, which is a form of registration. Unlike traditional correlation, we aim at…
Digital filters for recursively computing the discrete Fourier transform (DFT) and estimating the frequency spectrum of sampled signals are examined, with an emphasis on magnitude-response and numerical stability. In this tutorial-style…