  We present the saddle-point approximation for the effective Hamiltonian of
the quantum kink in two-dimensional linear sigma models to all orders in the
time-derivative expansion. We show how the effective Hamiltonian can be used to
obtain semiclassical soliton form factors, valid at momentum transfers of order
the soliton mass. Explicit results, however, hinge on finding an explicit
solution to a new wave-like partial differential equation, with a
time-dependent velocity and a forcing term that depend on the solution. In the
limit of small momentum transfer, the effective Hamiltonian reduces to the
expected form, namely H = (P^2 + M^2)^(1/2), where M is the one-loop corrected
soliton mass, and soliton form factors are given in terms of Fourier transforms
of the corresponding classical profiles.
