  The perturbed conformal field theories corresponding to the massive Symmetric
Space sine-Gordon soliton theories are identified by calculating the central
charge of the unperturbed conformal field theory and the conformal dimension of
the perturbation. They are described by an action with a positive-definite
kinetic term and a real potential term bounded from below, their equations of
motion are non-abelian affine Toda equations and, moreover, they exhibit a mass
gap. The unperturbed CFT corresponding to the compact symmetric space G/G_0 is
either the WZNW action for G_0 or the gauged WZNW action for a coset of the
form G_0/U(1)^p. The quantum integrability of the theories that describe
perturbations of a WZNW action, named Split models, is established by showing
that they have quantum conserved quantities of spin +3 and -3. Together with
the already known results for the other massive theories associated with the
non-abelian affine Toda equations, the Homogeneous sine-Gordon theories, this
supports the conjecture that all the massive Symmetric Space sine-Gordon
theories will be quantum integrable and, hence, will admit a factorizable
S-matrix. The general features of the soliton spectrum are discussed, and some
explicit soliton solutions for the Split models are constructed. In general,
the solitons will carry both topological charges and abelian Noether charges.
Moreover, the spectrum is expected to include stable and unstable particles.
