29 citations · 165 across the 21 of their papers we have counts for
5 papers · 1 filter
Numerical Methods for Fast Nonlinear Fourier Transformation, Part I: Exponential Runge-Kutta and Linear Multistep Methods
Vishal Vaibhav
The main objective of this series of papers is to explore the entire landscape of numerical methods for fast nonlinear Fourier transformation (NFT) within the class of integrators…
Nonlinearly Bandlimited Signals
Vishal Vaibhav
In this paper, we study the inverse scattering problem for a class of signals that have a compactly supported reflection coefficient. The problem boils down to the solution of the…
Discrete Darboux Transformation for Ablowitz-Ladik Systems Derived from Numerical Discretization of Zakharov-Shabat Scattering Problem
Vishal Vaibhav
The numerical discretization of the Zakharov-Shabat Scattering problem using integrators based on the implicit Euler method, trapezoidal rule and the split-Magnus method yield disc…
Nonlinear Fourier Transform of Time-Limited and One-sided Signals
Vishal Vaibhav
In this article, we study the properties of the nonlinear Fourier spectrum in order to gain better control of the temporal support of the signals synthesized using the inverse nonl…
New method of bandlimited extrapolation
Vishal Vaibhav
The paper deals with numerical solution of the Fredholm integral equation associated with the classical problem of extrapolating bandlimited functions known on to the enti…