The dynamics of weakly nonlinear wave packets in deep water can be for instance described by the nonlinear Schrödinger equation (NLS). As a deterministic and integrable evolution equation, the NLS enables to determine exact initial or boundary conditions to study the weakly nonlinear motion of a wave packet of interest. Among a vast family of solutions, we will focus our attention on the hydrodynamics of stationary deep water wave packets. The latter can be for instance described by means of hyperbolic or elliptic functions (sech, cnoidal & dnoidal expressions). Experiments have been conducted in different uni-directional wave facilities in order to validate the weakly nonlinear approach. The experimental wave profiles show a very good agreement with NLS predictions for various wave steepness values. The generic effect of wave dissipation in the considered framework will be discussed as well.