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

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.