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We study static kink solutions in a generalized two-dimensional dilatongravity model, where the kinetic term of the dilaton is generalized to be anarbitrary function of the canonical one $\mathcal X= -\frac12 (\nabla\varphi)^2$, say $\mathcal F(\mathcal X)$, and the kink is generated by acanonical scalar matter field $\phi$. It is found that for arbitrary $\mathcalF(\mathcal X)$, the background field equations have a simple first-orderformalism, and the linear perturbation equation can always be written as aSchr\"odinger-like equation with factorizable Hamiltonian operator. Afterchoosing appropriate $\mathcal F(\mathcal X)$ and superpotential, we obtain asine-Gordon type kink solution with pure AdS$_2$ metric. The linearperturbation equation of this solution becomes exactly solvable if one of themodel parameter takes a critical value.

Kink solutions in generalized 2D dilaton gravity