  Critical behavior of solitonic waveforms of Bose-Einstein condensates in
optical lattices (OL) has been studied in the framework of continuous
mean-field equation. In 2D and 3D OLs bright matter-wave solitons undergo
abrupt delocalization as the strength of the OL is decreased below some
critical value. Similar delocalizing transition happens when the coefficient of
nonlinearity crosses the critical value. Contrarily, bright solitons in 1D OLs
retain their integrity over the whole range of parameter variations. The
interpretation of the phenomenon in terms of quantum bound states in the
effective potential is proposed.
