  Using a proposed numerical technique for calculating anomalous Green's
functions characteristic of superconductivity, we show that the low-lying
excitations in a wide parameter and doping region of the two-dimensional
$t$$-$$J$ model are well described by the picture of dressed Bogoliubov
quasiparticles in the BCS pairing theory. The pairing occurs predominantly in
$d_{x^2-y^2}$-wave channel and the energy gap has a size
$\Delta_d$$\simeq$$0.15J$$-0.27J$ between quarter and half fillings. Opening of
the superconducting gap in the photoemission and inverse-photoemission spectrum
is demonstrated.
