Kink solutions in generalized 2D dilaton gravity

We study static kink solutions in a generalized two-dimensional dilaton gravity model, where the kinetic term of the dilaton is generalized to be an arbitrary function of the canonical one chi = -1/2(del phi)(2), say F(chi), and the kink is generated by a canonical scalar matter field phi. It is found that for arbitrary F(chi), the background field equations have a simple first-order formalism, and the linear perturbation equation can always be written as a Schrodinger-like equation with factorizable Hamiltonian operator. After choosing appropriate F(chi) and superpotential, we obtain a sine-Gordon type kink solution with pure AdS(2) metric. The linear perturbation issue of this solution becomes an exactly solvable conformal quantum mechanics problem, if one of the model parameter takes a critical value.