Abstract
The Sasa-satsuma (SS) dynamical equation interpret propagation of ultra-short and femto-second pulses in optical fibers. This dynamical model has important physical significance. In this article, two mathematical techniques namely, improved F-expansion and improved auxiliary methods are utilized to construct the several types of solitons such as dark soliton, bright soliton, periodic soliton, Elliptic function and solitary waves solutions of Sasa-satsuma dynamical equation. These results have imperative applications in sciences and other fields, and constructive to recognize the physical structure of this complex dynamical model. The computing work and obtained results show the influence and effectiveness of current methods.