A fast decaying solution to the modified Novikov--Veselov equation with a one-point singularity

TL;DR

This paper constructs an explicit, rapidly decaying solution with a singularity for the modified Novikov--Veselov equation using geometric transformations and minimal surface theory.

Contribution

It introduces a novel explicit solution with a singularity for the modified Novikov--Veselov equation via the Moutard transformation and minimal surface geometry.

Findings

Explicit example of a fast decaying solution with a one-point singularity.

Utilizes geometric interpretation of Moutard transformation.

Connects minimal surface theory to solutions of the equation.

Abstract

We present an explicit example of a fast decaying solution to the modified Novikov--Veselov equation with a one-point singularity in the space-time. It is constructed by using the geometrical interpretation of the Moutard transformation of solutions to this equation and the Enneper minimal surface.