  We associate a periodic two-dimensional Schrodinger operator to every
Lagrangian torus in CP^2 and define the spectral curve of a torus as the
Floquet spectrum of this operator on the zero energy level. In this event
minimal Lagrangian tori correspond to potential operators. We show that
Novikov-Veselov hierarchy of equations induces integrable deformations of
minimal Lagrangian torus in CP^2 preserving the spectral curve. We also show
that the highest flows on the space of smooth periodic solutions of the
Tzizeica equation are given by the Novikov-Veselov hierarchy.
