Absence of sufficiently localized traveling wave solutions for the Novikov-Veselov equation at zero energy

We demonstrate that the Novikov.Veselov equation (a (2+1)-dimensional analog of KdV) at zero energy does not possess solitons with the space localization stronger than O(|x|^{-4})

Absence of traveling wave solutions of conductivity type for the Novikov-Veselov equations at zero energy

We prove that the Novikov-Veselov equation (an analog of KdV in dimension 2 + 1) at zero energy does not have sufficiently localized soliton solutions of conductivity type

A large time asymptotics for the solution of the Cauchy problem for the Novikov-Veselov equation at negative energy with non-singular scattering data

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 Schr\"odinger equation at negative energy. We show that the solution of the Cauchy problem for this equation with non--singular scattering data behaves asymptotically as \frac{\const}{t^{3/4}} in the uniform norm at large times $t$. We also present some arguments which indicate that this asymptotics is optimal

Absence of solitons with sufficient algebraic localization for the Novikov-Veselov equation at nonzero energy

We show that the Novikov--Veselov equation (an analog of KdV in dimension 2 + 1) at positive and negative energies does not have solitons with the space localization stronger than O(|x|^{-3}) as |x| \to \infty

Large time asymptotics for the Grinevich-Zakharov potentials

In this article we show that the large time asymptotics for the Grinevich-Zakharov rational solutions of the Novikov-Veselov equation at positive energy (an analog of KdV in 2+1 dimensions) is given by a finite sum of localized travel waves (solitons)

Absence of exponentially localized solitons for the Novikov--Veselov equation at negative energy

International audienceWe show that Novikov--Veselov equation (an analog of KdV in dimension 2 + 1) does not have exponentially localized solitons at negative energy

Ergodicity of the underdamped mean-field Langevin dynamics

We study the long time behavior of an underdamped mean-field Langevin (MFL) equation, and provide a general convergence as well as an exponential convergence rate result under different conditions. The results on the MFL equation can be applied to study the convergence of the Hamiltonian gradient descent algorithm for the overparametrized optimization. We then provide a numerical example of the algorithm to train a generative adversarial networks (GAN).Comment: 29 pages, 2 figure

Anisotropic compressed sensing for non-Cartesian MRI acquisitions

In the present note we develop some theoretical results in the theory of anisotropic compressed sensing that allow to take structured sparsity and variable density structured sampling into account. We expect that the obtained results will be useful to derive explicit expressions for optimal sampling strategies in the non-Cartesian (radial, spiral, etc.) setting in MRI