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

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.

arXiv comment18 pages

References in corpus (8)

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• Two-dimensional Dirac operator and surface theory
• Darboux transformation for the modified Veselov-Novikov equation
• Weierstrass representations for surfaces in 4D spaces and their integrable deformations via DS hierarchy
• Two-dimensional Schroedinger operators with fast decaying potential and multidimensional $L_2$-kernel
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Cited by in corpus (4)

• Construction of exact solutions of nonlinear PDE via dressing chain in 3D
• On a class of exact solutions of the Ishimori equation
• Surfaces via spinors and soliton equations
• On a formation of singularities of solutions to soliton equations represented by L,A,B-triples