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In this letter, via the Darboux transformation method we construct newanalytic soliton solutions for the Sasa-Satsuma equation which describes thefemtosecond pulses propagation in a monomode fiber. We reveal that twodifferent types of femtosecond solitons, i.e., the anti-dark (AD) andMexican-hat (MH) solitons, can form on a continuous wave (CW) background, andnumerically study their stability under small initial perturbations. Differentfrom the common bright and dark solitons, the AD and MH solitons can exhibitboth the resonant and elastic interactions, as well as variouspartially/completely inelastic interactions which are composed of such twofundamental interactions. In addition, we find that the energy exchange betweensome interacting soliton and the CW background may lead to one AD solitonchanging into an MH one, or one MH soliton into an AD one.

Anti-dark and Mexican-hat solitons in the Sasa-Satsuma equation on the continuous wave background