The quasi-one-dimensional chains of halogen-bridged mixed-valence platinum complexes (HMPC) have characteristic twofold degeneracy similar to the trans isomer of polyacetylene, which strongly suggests the presence of soliton-like excitations in HMPC. It is shown that the microscopic Hamiltonian proposed by Ichinose for HMPC, which naturally is different from the Su-Schrieffer-Heeger model of trans -polyacetylene, leads to the Takayama-Lin-Liu-Maki Hamiltonian when the continuum limit is taken. This theoretical result implies that we can expect various soliton processes found in trans -polyacetylene to take place in HMPC as well, though such experimental evidences are scarce as yet.