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The Moutard Transformation for the Davey–Stewartson II Equation and Its Geometrical Meaning

Authors
  • Taimanov, I. A.1, 2
  • 1 Novosibirsk State University, Novosibirsk, 630090, Russia , Novosibirsk (Russia)
  • 2 Sobolev Institute of Mathematics, Siberian Branch of Russian Academy of Sciences, Novosibirsk, 630090, Russia , Novosibirsk (Russia)
Type
Published Article
Journal
Mathematical Notes
Publisher
Pleiades Publishing
Publication Date
Nov 01, 2021
Volume
110
Issue
5-6
Pages
754–766
Identifiers
DOI: 10.1134/S0001434621110122
Source
Springer Nature
Keywords
Disciplines
  • article
License
Yellow

Abstract

Abstract The Moutard transformation for the solutions of the Davey–Stewartson II equation is constructed. It is geometrically interpreted using the spinor (Weierstrass) representation of surfaces in four-dimensional Euclidean space. Examples of solutions that have smooth fast decaying initial data and lose regularity in finite time are constructed by using the Moutard transformation and minimal surfaces.

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