  We investigate generalized Jackiw-Teitelboim gravity, coupling the dilaton
field with two scalar matter fields. We obtain the equations of motion of the
fields and investigate the linear perturbation of the solutions in general. We
study two specific situations that allow analytic solutions with topological
behavior and check how the dilaton field, the warp factor and Ricci scalar
behave. In particular, we have shown how the parameters can be used to modify
the structure of the solutions. Moreover, the perturbations are in general
described by intricate coupled differential equations, but in some specific
cases we could construct the corresponding zero modes analytically.
