  The subject of the work is the stabilization of two-dimensional (2D)
two-component (vector) solitons, in media with the attractive cubic
nonlinearity, against the collapse by a linear lattice (LL, which is induced by
a periodic modulation of the refractive index in optics, or created as an
optical lattice in BEC), or by a nonlinear lattice (NL, induced by a periodic
modulation of the nonlinearity coefficient). We demonstrate that, due to the
XPM (cross-phase-modulation) coupling between the components, the LL or NL
acting on a single component is sufficient for the stabilization of vector
solitons, that include a component for which the self-focusing medium is
uniform. In the case of the LL, the vector solitons are stable almost in their
entire existence domain, while the NL can only stabilize the solitons in which
the component affected by the lattice carries the norm which is comparable to,
or larger than the norm of the component in the uniform medium.
