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

TL;DR

This paper proves that the Novikov-Veselov equation at zero energy cannot have highly localized traveling wave solutions, indicating limitations on soliton existence in this context.

Contribution

It establishes a nonexistence result for strongly localized solitons in the Novikov-Veselov equation at zero energy, extending understanding of soliton behavior in higher dimensions.

Findings

No solitons with localization stronger than O(|x|^{-4}) exist at zero energy

The result applies to the (2+1)-dimensional Novikov-Veselov equation

Limits the types of localized solutions possible for this equation

Abstract

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}).