Phase competition and excitations in the one-dimensional neutral-ionic transition systems are theoretically studied comprehensively. From the semiclassical treatment of the bosonized Hamiltonian, we examine the competition among the neutral (N), ferroelectric-ionic (I$_mathrm{ferro}$) and paraelectric-ionic (I$_mathrm{para}$) states. The phase transitions between them can become first-order when the fluctuation-induced higher-order commensurability potential is considered. In particular, the description of the first-order phase boundary between N and I$_mathrm{ferro}$ enables us to analyze N-I$_mathrm{ferro}$ domain walls. Soliton excitations in the three phases are described explicitly and their formation energies are evaluated across the phase boundaries. The characters of the soliton and domain-wall excitations are classified in terms of the topological charge and spin. The relevance to the experimental observations in the molecular neutral-ionic transition systems is discussed. We ascribe the pressure-induced crossover in tetrathiafulvalene-$p$-chloranil (TTF-CA) at a high-temperature region to that from the N to the I$_mathrm{para}$ state, and discuss its consequence.
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