  Self-gravitating kink solutions of a two-dimensional dilaton gravity are
revisited in this work. Analytical kink solutions are derived from a concise
superpotential formalism of the dynamical equations. A general analysis on the
linear stability is conducted for an arbitrary static solution of the model.
After gauge fixing, a Schr\"odinger-like equation with factorizable Hamiltonian
operator is obtained, which ensures the linear stability of the solution.
