Finite-gap solutions of the modified Novikov-Veselov equations: their spectral properties and applications

TL;DR

This paper constructs finite-gap solutions for the modified Novikov-Veselov equations, analyzes their spectral properties, and explores their connections to soliton deformations of tori and the Willmore conjecture.

Contribution

It introduces a method to construct finite-gap solutions and links these solutions to spectral theory, soliton deformations, and geometric conjectures.

Findings

Finite-gap solutions are explicitly constructed.

Spectral properties of these solutions are characterized.

Connections to soliton deformations of tori and the Willmore conjecture are established.

Abstract

We construct finite-gap solutions to the modified Novikov-Veselov equations, describe their spectral properties and the reduction to the modified Korteweg--de Vries equation and explain its relation to soliton deformations of tori and the Willmore conjecture.