  The Sasa-Satsuma equation, a higher-order nonlinear Schr\"{o}dinger equation,
is an important integrable equation, which displays the propagation of
femtosecond pulses in optical fibers. In this paper, we investigate a
generalized Sasa-Satsuma(gSS) equation. The Darboux transformation(DT) for the
focusing and defocusing gSS equation is constructed. By using the DT, various
of soliton solutions for the generalized Sasa-Satsuma equation are derived,
including hump-type, breather-type and periodic soliton. Dynamics properties
and asymptotic behavior of these soliton solutions are analyzed. Infinite
number conservation laws and conserved quantities for the gSS equation are
obtained.
