29 citations · 165 across the 21 of their papers we have counts for
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A Chebyshev Spectral Method for Nonlinear Fourier Transform: Norming Constants
Vishal Vaibhav
In this paper, we present a Chebyshev based spectral method for the computation of the Jost solutions corresponding to complex values of the spectral parameter in the Zakharov--Sha…
A Fast Chebyshev Spectral Method for Nonlinear Fourier Transform
Vishal Vaibhav
In this letter, we present a fast and well-conditioned spectral method based on the Chebyshev polynomials for computing the continuous part of the nonlinear Fourier spectrum. The a…
Fast Nonlinear Fourier Transform using Chebyshev Polynomials
Vishal Vaibhav
We explore the class of exponential integrators known as exponential time differencing (ETD) method in this letter to design low complexity nonlinear Fourier transform (NFT) algori…
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…
Higher Order Convergent Fast Nonlinear Fourier Transform
Vishal Vaibhav
It is demonstrated is this letter that linear multistep methods for integrating ordinary differential equations can be used to develop a family of fast forward scattering algorithm…
Exact Solution of the Zakharov-Shabat Scattering Problem for Doubly-Truncated Multi-Soliton Potentials
V. Vaibhav
Recent studies have revealed that multi-soliton solutions of the nonlinear Schrödinger equation, as carriers of information, offer a promising solution to the problem of nonlinear…
Fast Inverse Nonlinear Fourier Transformation using Exponential One-Step Methods, Part I: Darboux Transformation
Vishal Vaibhav
This paper considers the non-Hermitian Zakharov-Shabat (ZS) scattering problem which forms the basis for defining the SU-nonlinear Fourier transformation (NFT). The theoretica…
On the nonreflecting boundary operators for the general two dimensional Schrödinger equation
Vishal Vaibhav
Of the two main objectives we pursue in this paper, the first one consists in the studying operators of the form where $\tri…