  We developed a comprehensive semiclassical theory of solitons in one
dimensional systems at BCS-BEC crossover to provide a semiclassical explanation
of their excitation spectra. Our semiclassical results agree well with the
exact solutions on both the deep BCS and deep BEC side and explain
qualitatively the smooth crossover between them. Especially, we showed that the
minimum energy of the $S=1/2$ excitation is achieved exactly at the Fermi
momentum $k_F=\pi n/2$, where $nm_F$ ($m_F$ is the mass of the fermionic atom)
is the total mass density of the system. This momentum remains unchanged along
the whole crossover, whether the mass is contained in the bosonic molecules as
on the deep BEC side or in the fermionic atoms as on the deep BCS side. This
phenomenon comes about as a result of a special feature of one dimensional
systems that the conventional quasiparticle is not stable with respect to
soliton formation. It is valid not only in exactly solvable models but also on
the level of semiclassical theory. Besides, we also resolved the inconsistency
of existing semiclassical theory with the exact solution of soliton-like $S=0$
excitations on the deep BCS side by a new proposal of soliton configuration.
