We employed micro-focused Brillouin light scattering to study the amplification of the thermal spin wave eigenmodes by means of a pure spin current, generated by the spin-Hall effect, in a transversely magnetized Pt(4 nm)/NiFe(4 nm)/SiO2(5 nm) layered nanowire with lateral dimensions 500 x 2750 nm(2). The frequency and the cross section of both the center (fundamental) and the edge spin wave modes have been measured as a function of the intensity of the injected dc electric current. The frequency of both modes exhibits a clear redshift while their cross section is greatly enhanced on increasing the intensity of the injected dc. A threshold-like behavior is observed for a value of the injected dc of 2.8 mA. Interestingly, an additional mode, localized in the central part of the nanowire, appears at higher frequency on increasing the intensity of the injected dc above the threshold value. Micromagnetic simulations were used to quantitatively reproduce the experimental results and to investigate the complex non-linear dynamics induced by the spin-Hall effect, including the modification of the spatial profile of the spin wave modes and the appearance of the extra mode above the threshold. (C) 2015 AIP Publishing LLC.