相关论文: The Novikov-Veselov Equation: Theory and Computati…
Using the inverse scattering method, we construct global solutions to the Novikov-Veselov equation for real-valued decaying initial data q with the property that the associated Schrodinger operator with potential q is nonnegative. Such…
The Novikov-Veselov (NV) equation is a (2+1)-dimensional nonlinear evolution equation that generalizes the (1+1)-dimensional Korteweg-deVries (KdV) equation. Solution of the NV equation using the inverse scattering method has been discussed…
The inverse scattering method for the Novikov-Veselov equation is studied for a larger class of Schr\"odinger potentials than could be handled previously. Previous work concerns so-called conductivity type potentials, which have a bounded…
In this paper we continue our study on the Cauchy problem for the two-dimensional Novikov-Veselov (NV) equation, integrable via the inverse scattering transform for the two dimensional Schr\"odinger operator at a fixed energy parameter.…
We define scattering data for the Newton equation in a potential $V\in C^2(\R^n,\R)$, $n\ge2$, that decays at infinity like $r^{-\alpha}$ for some $\alpha\in (0,1]$. We provide estimates on the scattering solutions and scattering data and…
The cluster reduction method for the Yakubovsky equations in configuration space is used for calculations of zero-energy scattering in four-nucleon system. The main idea of the method consists in making use of expansions for the Yakubovsky…
This paper corrects several errors in the author's previous papers (Journal of Spectral Theory 2016, Analysis and PDE 2014) on the Davey-Stewartson II (DS II) and modified Novikov-Veselov (mNV) equations. In each of these papers a proof was…
The numerical algorithm of the inverse quantum scattering is developed. This algorithm is based on the Marchenko theory, and includes three steps. The first one is the algebraic Pade approximation of the unitary S-matrix, what is realized…
We consider the inverse scattering problem at fixed and sufficiently large energy for the nonrelativistic and relativistic Newton equation in $\R^n$, $n \ge 2$, with a smooth and short range electromagnetic field $(V,B)$. Using results of…
We use the inverse scattering method to construct classical solutions for the Novikov-Veselov (NV) equation, solving a problem posed by Lassas, Mueller, Siltanen, and Stahel. We exploit Bogadanov's Miura-type map which transforms solutions…
We present an explicit example of a fast decaying solution to the modified Novikov--Veselov equation with a one-point singularity in the space-time. It is constructed by using the geometrical interpretation of the Moutard transformation of…
The direct and inverse scattering problems on the full line are analyzed for a first-order system of ordinary linear differential equations associated with the derivative nonlinear Schr\"odinger equation and related equations. The system…
An example of full solution of the inverse scattering problem on the half line is presented. For this purpose, a simple analytically solvable model system (Morse potential) is used, which is expected to be a reasonable approximation to a…
Inverse scattering and spectral one-dimensional problems are discussed systematically in a self-contained way. Many novel results, due to the author are presented. The classical results are often presented in a new way. Several highlights…
In the context of the Cauchy problem for the Korteweg-de Vries equation we extend the inverse scattering transform to initial data that behave at plus infinity like a sum of Wigner-von Neumann type potentials with small coupling constants.…
In the present paper we are concerned with the Novikov--Veselov equation at negative energy, i.e. with the $ (2 + 1) $--dimensional analog of the KdV equation integrable by the method of inverse scattering for the two--dimensional…
We study the energy-critical nonlinear wave equation in the presence of an inverse-square potential in dimensions three and four. In the defocusing case, we prove that arbitrary initial data in the energy space lead to global solutions that…
In this paper we show that in two-body scattering the scattering matrix at a fixed energy determines real-valued exponentially decreasing potentials. This result has been proved by Novikov previously, see also the work of Novikov and…
We present an iterative algorithm to compute numerical approximations of the potential for the Schr\"odinger operator from scattering data. Four different types of scattering data are used as follows: fixed energy, fixed incident angle,…
A construction of blowing up solutions to the modified Novikov-Veselov equation is proposed. It is based on the Moutard transformation of two-dimensional Dirac operators and its geometrical interpretation via surface geometry. An explicit…