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The Moutard transform is constructed for the solutions of theDavey-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 solutionsare constructed that have smooth, rapidly decreasing initial data and losetheir regularity in a finite time.

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