29 citations · 165 across the 21 of their papers we have counts for
21 papers
End-to-End Argument Mining through Autoregressive Argumentative Structure Prediction
Nilmadhab Das, Vishal Vaibhav, Yash Sunil Choudhary +2
Argument Mining (AM) helps in automating the extraction of complex argumentative structures such as Argument Components (ACs) like Premise, Claim etc. and Argumentative Relations (…
Nonreflecting Boundary Condition for the free Schrödinger equation for hyperrectangular computational domains
Samardhi Yadav, Vishal Vaibhav
In this article, we discuss the efficient ways of implementing the transparent boundary condition (TBC) and its various approximations for the free Schrödinger equation on a hyperr…
Transparent boundary condition and its high frequency approximation for the Schrödinger equation on a rectangular computational domain
Samardhi Yadav, Vishal Vaibhav
This paper addresses the numerical implementation of the transparent boundary condition (TBC) and its various approximations for the free Schrödinger equation on a rectangular comp…
Transparent boundary condition and its effectively local approximation for the Schrödinger equation on a rectangular computational domain
Samardhi Yadav, Vishal Vaibhav
The transparent boundary condition for the free Schrödinger equation on a rectangular computational domain requires implementation of an operator of the form $\sqrt{\partial_t-i\tr…
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…
Efficient Nonlinear Fourier Transform Algorithms of Order Four on Equispaced Grid
Vishal Vaibhav
We explore two classes of exponential integrators in this letter to design nonlinear Fourier transform (NFT) algorithms with a desired accuracy-complexity trade-off and a convergen…
Darboux Transformation: New Identities
Vishal Vaibhav
This letter reports some new identities for multisoliton potentials that are based on the explicit representation provided by the Darboux matrix. These identities can be used to co…
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…
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 Transform
Vishal Vaibhav
This paper considers the non-Hermitian Zakharov-Shabat (ZS) scattering problem which forms the basis for defining the SU-nonlinear Fourier transform (NFT). The theoretical und…
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…
Fast Inverse Nonlinear Fourier Transforms for Continuous Spectra of Zakharov-Shabat Type
Sander Wahls, Vishal Vaibhav
The nonlinear Schrödinger equation (NSE) is well-known to model an ideal fiber-optic communication channel. Even though the NSE is a nonlinear evolution equation, it can be solved…
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…
A measurement-induced optical Kerr interaction
Seckin Sefi, Vishal Vaibhav, Peter van Loock
We present a method for implementing a weak optical Kerr interaction (single-mode Kerr Hamiltonian) in a measurement-based fashion using the common set of universal elementary inte…