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

Abstract

In this note we show that the Novikov-Veselov equation at positive energy (an analog of KdV in 2+1 dimensions) has no exponentially localized solitons ( in the two-dimensional sense).

References in corpus (2)

• Transparent Potentials at Fixed Energy in Dimension Two. Fixed-Energy Dispersion Relations for the Fast Decaying Potentials
• Absence of exponentially localized solitons for the Novikov--Veselov equation at negative energy

Cited by in corpus (8)

• Explicit formulas and global uniqueness for phaseless inverse scattering in multidimensions
• A large time asymptotics for the solution of the Cauchy problem for the Novikov-Veselov equation at negative energy with non-singular scattering data
• Absence of exponentially localized solitons for the Novikov--Veselov equation at negative energy
• Large time asymptotics for the Grinevich-Zakharov potentials
• Numerical study of blow-up and stability of line solitons for the Novikov-Veselov equation
• The Cauchy problem for the generalized hyperbolic Novikov-Veselov equation via the Moutard symmetries
• Lax-Sato formulation of the Novikov-Veselov Hierarchy
• Absence of sufficiently localized traveling wave solutions for the Novikov-Veselov equation at zero energy