In this article, we study the dynamics of optical soliton (Gausson) pulses in waveguides based on ENZ-materials. The theoretical approach used is based on the handling of the non-linear Schro center dot dinger's equation using the moment method. The physical system studied is dissipative. The loss of energy in the waveguide, which can be explained by the existence of imaginary parts of the refractive index of the ENZ-material, is negligible because permittivity of ENZ-materials is low. In addition, we show that self-phase modulation results in the increase of chirp during the propagation of such Gaussons.