  We investigate ground-state properties and quantum phase transitions in the
one-dimensional S=1 spin-orbital model relevant to cubic vanadates. Using the
density matrix renormalization group, we compute the ground-state energy, the
magnetization and the correlation functions for different values of the Hund's
coupling $J_H$ and the external magnetic field. It is found that the
magnetization jumps at a certain critical field, which is a hallmark of the
field-induced first-order phase transition. The phase transition driven by
$J_H$ is also of first order. We also consider how the lattice-induced
ferro-type interaction between orbitals modifies the phase diagram, and discuss
the results in a context of the first-order phase transition observed in
YVO$_3$ at 77K.
