The Moutard transformation for the Davey-Stewartson II equation and its geometrical meaning

TL;DR

This paper develops a Moutard transformation for the Davey-Stewartson II equation, interprets it geometrically via surface representations, and constructs solutions with finite-time loss of regularity.

Contribution

It introduces a novel Moutard transform for the DS II equation and links it to geometric surface theory, providing new solution construction methods.

Findings

Constructed solutions with smooth, rapidly decreasing initial data

Demonstrated finite-time loss of regularity in solutions

Connected integrable PDEs with differential geometry concepts

Abstract

The Moutard transform is constructed for the solutions of the Davey-Stewartson II equation. It is geometrically interpreted using the spinor (Weierstrass) representation of surfaces in four-dimensional Euclidean space. Using the Moutard transformation and minimal surfaces, examples of solutions are constructed that have smooth, rapidly decreasing initial data and lose their regularity in a finite time.