Related papers: Numerical inverse scattering for the sine-Gordon e…
Initially, we derive a nonlinear integral equation for the vacuum counting function of the spin 1/2-XYZ chain in the {\it disordered regime}, thus paralleling similar results by Kl\"umper \cite{KLU}, achieved through a different technique…
We propose Gauss-Newton's method in function space for the solution of the Navier-Stokes equations in the physics-informed neural network (PINN) framework. Upon discretization, this yields a natural gradient method that provably mimics the…
This article deals with the numerical integration in time of nonlinear Schr\"odinger equations. The main application is the numerical simulation of rotating Bose-Einstein condensates. The authors perform a change of unknown so that the…
We present a novel numerical method to the time-harmonic inverse medium scattering problem of recovering the refractive index from near-field scattered data. The approach consists of two stages, one pruning step of detecting the scatterer…
This work is concerned with an inverse elastic scattering problem of identifying the unknown rigid obstacle embedded in an open space filled with a homogeneous and isotropic elastic medium. A Newton-type iteration method relying on the…
An inexact Newton type method for numerical minimization of convex piecewise quadratic functions is considered and its convergence is analyzed. Earlier, a similar method was successfully applied to optimizaton problems arising in numerical…
In this article we present robust, efficient and accurate fully implicit time-stepping schemes and nonlinear solvers for systems of reaction-diffusion equations. The applications of reaction-diffusion systems is abundant in the literature,…
A generalised inverse scattering method has been developed for arbitrary n dimensional Lax equations. Subsequently, the method has been used to obtain N soliton solutions of a vector higher order nonlinear Schrodinger equation, proposed by…
In this paper, we present a rigorous study of the direct scattering problem that arises from the complete integrability of the Benjamin--Ono (BO) equation. In particular, we establish existence, uniqueness, and asymptotic properties of the…
We introduce numerical solvers for the steady-state Boltzmann equation based on the symmetric Gauss-Seidel (SGS) method. Due to the quadratic collision operator in the Boltzmann equation, the SGS method requires solving a nonlinear system…
This paper is concerned with the direct and inverse acoustic or electromagnetic scattering problems by a locally perturbed, perfectly reflecting, infinite plane (which is called a locally rough surface in this paper). We propose a novel…
In this work we consider stochastic gradient descent (SGD) for solving linear inverse problems in Banach spaces. SGD and its variants have been established as one of the most successful optimisation methods in machine learning, imaging and…
We show the relationship between the strongly non-linear limit (also termed the dispersionless or the Whitham limit) of the macroscopic fluctuation theory of certain statistical models and the inverse scattering method. We show that in the…
By employing a novel generalization of the inverse scattering transform method known as the unified transform or Fokas method, it can be shown that the solution of certain physically significant boundary value problems for the elliptic…
We examine the connection between the nonlinear integral equation (NLIE) derived from light-cone lattice and sine-Gordon quantum field theory, considered as a perturbed c=1 conformal field theory. After clarifying some delicate points of…
This paper is concerned with the nonnegative inverse eigenvalue problem of finding a nonnegative matrix such that its spectrum is the prescribed self-conjugate set of complex numbers. We first reformulate the nonnegative inverse eigenvalue…
We summarize efforts at NIST to implement quantum computation using trapped ions, based on a scheme proposed by J.I. Cirac and P. Zoller (Innsbruck University). The use of quantum logic to create entangled states, which can maximize the…
In this paper, we consider the long time behavior of solution to the quadratic gauge invariant nonlinear Klein-Gordon equation (NLKG) in two space dimensions. For a given asymptotic profile, we construct a solution to (NLKG) which converges…
We introduce a novel method for encoding integers using smooth real-valued functions whose integral properties implicitly reflect discrete quantities. In contrast to classical representations, where the integer appears as an explicit…
This paper aims to develop a linearly implicit structure-preserving numerical scheme for the space fractional sine-Gordon equation, which is based on the newly developed invariant energy quadratization method. First, we reformulate the…