  In this letter, via the Darboux transformation method we construct new
analytic soliton solutions for the Sasa-Satsuma equation which describes the
femtosecond pulses propagation in a monomode fiber. We reveal that two
different types of femtosecond solitons, i.e., the anti-dark (AD) and
Mexican-hat (MH) solitons, can form on a continuous wave (CW) background, and
numerically study their stability under small initial perturbations. Different
from the common bright and dark solitons, the AD and MH solitons can exhibit
both the resonant and elastic interactions, as well as various
partially/completely inelastic interactions which are composed of such two
fundamental interactions. In addition, we find that the energy exchange between
some interacting soliton and the CW background may lead to one AD soliton
changing into an MH one, or one MH soliton into an AD one.
