The Moutard transform is constructed for the solutions of Davey-Stewartson II equation. It geometrically interpreted using spinor (Weierstrass) representation surfaces in four-dimensional Euclidean space. Using transformation and minimal surfaces, examples are that have smooth, rapidly decreasing initial data lose their regularity a finite time.

Michael S. Saag, MD; Rajesh T. Gandhi, Jennifer F. Hoy, MBBS; Raphael J. Landovitz, Melanie A. Thompson, Paul E. Sax, Davey M. Smith, Constance Benson, Susan P. Buchbinder, Carlos del Rio, Joseph Eron Jr, Gerd Fätkenheuer, Huldrych Günthard, Jean-Michel Molina, Donna Jacobsen, BS; Volberding, MD

Flavio Seno, Cristian Micheletti, Amos Maritan and Jayanth R. Banavar (1) Dipartimento di Fisica, Università di Padova, Via Marzolo 8,35131 Padova, Italy and INFM (2) International School for Advanced Studies (S.I.S.S.A.), Via Beirut 2-4, 34014 Trieste, Italy and INFM (3) Department of Physics and Center for Materials Physics, 104 Davey Laboratory, The Pennsylvania State University, University ...

Generalized Weierstrass representations for generic surfaces confor-mally immersed into four-dimensional Euclidean and pseudo-Euclidean spaces of different signatures are presented. Integrable deformations of surfaces in these spaces generated by the Davey-Stewartson hierarchy of integrable equations are proposed. Willmore functional of a surface is invariant under such deformations.