  We study a disordered system of interacting bosons described by the
Bose-Hubbard Hamiltonian with random tunneling amplitudes. We derive the
condition for the stability of the replica-symmetric solution for this model.
Following the scheme of de Almeida and Thouless, we determine if the solution
corresponds to the minimum of free energy by building the respective Hessian
matrix and checking its positive semidefiniteness. Thus, we find the
eigenvalues by postulating the set of eigenvectors based on their expected
symmetry, and require the eigenvalues to be non-negative. We evaluate the
spectrum numerically and identify matrix blocks that give rise to eigenvalues
that are always non-negative. Thus, we find a subset of eigenvalues coming from
decoupled subspaces that is sufficient to be checked as the stability
criterion. We also determine the stability of the phases present in the system,
finding that the disordered phase is stable, the glass phase is unstable, while
the superfluid phase has both stable and unstable parts.
