  By using the Moutard transformation of two-dimensional Schroedinger operators
we derive a procedure for constructing explicit examples of such operators with
rational fast decaying potentials and degenerate $L_2$-kernels (this
construction was sketched in arXiv:0706.3595) and show that if we take some of
these potentials as the Cauchy data for the Novikov-Veselov equation (a
two-dimensional version of the Korteweg-de Vries equation), then the
corresponding solutions blow up in a finite time
