Exact solutions to the motion of two charged particles in lineal gravity

We extend the canonical formalism for the motion of N particles in lineal gravity to include charges. Under suitable coordinate conditions and boundary conditions the Hamiltonian is defined as the spatial integral of the second derivative of the dilaton field which is given as a solution to the constraint equations. For a system of two particles the determining equation of the Hamiltonian (a kind of transcendental equation) is derived from the matching conditions for the dilaton field at the particlesʹ position. The canonical equations of motion are derived from this determining equation.