Formation of singularities of two-dimensional soliton equations represented by $L,A,B$-triples

We present a geometrical mechanism of the formation of singularities of modified Novikov-Veselov and Davey-Stewartson II equations. The singular solutions are constructed by means of surface theory. These systems are represented by $L,A,B$–triples and we discuss the relation of such a mechanism to the degeneration of the zero level discrete spectra of the corresponding $L$–operators.