Blowing up solutions of the modified Novikov-Veselov equation and minimal surfaces

TL;DR

This paper constructs explicit blowing up solutions for the modified Novikov-Veselov equation using Moutard transformations and minimal surface geometry, providing detailed examples based on the Enneper surface.

Contribution

It introduces a novel method to generate blowing up solutions via Moutard transformations linked to surface geometry, expanding the understanding of the equation's solution space.

Findings

Explicit blowing up solutions constructed using minimal surfaces.

Geometrical interpretation via surface geometry enhances solution understanding.

Detailed example with the Enneper minimal surface provided.

Abstract

A construction of blowing up solutions to the modified Novikov-Veselov equation is proposed. It is based on the Moutard transformation of two-dimensional Dirac operators and its geometrical interpretation via surface geometry. An explicit example of such a solution constructed by using the Enneper minimal surface is discussed in detail. This example was briefly announced in arXiv:1408.4723.