The Ozawa solution to the Davey--Stewartson II equations and surface theory

TL;DR

This paper links the Ozawa solution of the Davey--Stewartson II equation to surface theory, illustrating a soliton deformation of surfaces and explicitly describing the singularity at blow-up.

Contribution

It introduces a novel geometric interpretation of the Ozawa solution through surface deformations and explicitly characterizes the resulting singularities.

Findings

Ozawa solution causes surface singularities at blow-up

Explicit description of surface deformation linked to the Ozawa solution

Connects integrable PDE solutions with differential geometry

Abstract

We describe the Ozawa solution to the Davey--Stewartson II equation from the point of view of surface theory by presenting a soliton deformation of surfaces which is ruled by the Ozawa solution. The Ozawa solution blows up at certain moment and we describe explicitly the corresponding singularity of the deformed surface.