  Soliton solutions in scalar field theory defined on a two-dimensional Anti-de
Sitter background space-time are investigated. It is shown that the lowest
soliton excitation generically has frequency equal to the inverse radius of the
space-time. Analytic and numerical soliton solutions are determined in "phi to
the fourth" scalar field theory with a negative mass-squared. The classical
soliton mass is calculated as a function of the ratio of the square of the mass
scale of the field theory over the curvature of the space-time. For the case
that this ratio equals unity, the soliton excitation spectrum is determined
algebraically and the one-loop radiative correction to the soliton mass is
computed in the semi-classical approximation.
