Revisit on two-dimensional self-gravitating kinks: superpotential formalism and linear stability

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.