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

TL;DR

This paper proves that the Novikov--Veselov equation, a 2+1 dimensional analog of KdV, cannot have exponentially localized soliton solutions at negative energy levels.

Contribution

It establishes a nonexistence result for exponentially localized solitons in the Novikov--Veselov equation at negative energy, filling a gap in the understanding of its soliton solutions.

Findings

No exponentially localized solitons at negative energy

Extends understanding of soliton solutions in higher dimensions

Provides mathematical proof of nonexistence

Abstract

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