Large time asymptotics for the Grinevich-Zakharov potentials

TL;DR

This paper analyzes the large time behavior of Grinevich-Zakharov rational solutions to the Novikov-Veselov equation, revealing that they asymptotically decompose into a finite sum of solitons, similar to KdV dynamics.

Contribution

It demonstrates the asymptotic decomposition of solutions into solitons for the Novikov-Veselov equation at positive energy, extending understanding of 2+1 dimensional integrable systems.

Findings

Solutions decompose into finite soliton sums at large times

Asymptotic behavior parallels KdV soliton dynamics

Provides explicit description of large time asymptotics

Abstract

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).