  Approximate solutions of the Gross-Pitaevskii (GP) equation, obtained upon
neglection of the kinetic energy, are well known as Thomas-Fermi solutions.
They are characterized by the compensation of the local potential by the
collisional energy. In this article we consider exact solutions of the
GP-equation with this property and definite values of the kinetic energy, which
suggests the term "kinetic Thomas-Fermi" (KTF) solutions. We point out that a
large class of light-shift potentials gives rise to KTF-solutions. As
elementary examples, we consider one-dimensional and two-dimensional optical
lattice scenarios, obtained by means of the superposition of two, three and
four laser beams, and discuss the stability properties of the corresponding
KTF-solutions. A general method is proposed to excite two-dimensional
KTF-solutions in experiments by means of time-modulated light-shift potentials.
