In this paper, the nonlinear complex Hirota-dynamical modelNLCHMin which the third derivative term represents the self-interaction in the high-frequency subsystem is established. This model plays a vital role in plasma physics because there are agreements between the self-interaction in the highfrequency and the well- known self-focusing effect in plasma. Many soliton solutions to this equation model have been achieved perfectly using the solitary wave ansatz method (SWAM). Furthermore, in the same vein and related subject the extended simple equation method (ESEM) has been applied perfectly to achieve new perception of soliton solutions to this model. A good isomorphic between the achieved results and that achieved previous by other authors have been listed.