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

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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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Authors and Affiliations

  1. Novosibirsk State University, Novosibirsk, 630090, Russia

    I. A. Taimanov

  2. Sobolev Institute of Mathematics, Siberian Branch of Russian Academy of Sciences, Novosibirsk, 630090, Russia

    I. A. Taimanov

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  1. I. A. Taimanov
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Correspondence to I. A. Taimanov.

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Translated from Matematicheskie Zametki, 2021, Vol. 110, pp. 751–765 https://doi.org/10.4213/mzm13246.

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Taimanov, I.A. The Moutard Transformation for the Davey–Stewartson II Equation and Its Geometrical Meaning. Math Notes 110, 754–766 (2021). https://doi.org/10.1134/S0001434621110122

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  • DOI: https://doi.org/10.1134/S0001434621110122

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