[en] In the continuum approximation the linear chain of interacting particles with the potential ''on site'' of the type of φ⁴ and φ⁴+φ⁶ with γφ dissipation term and f constant force in the equation of motion is considered. The similar-type solution of the latter has been derived as a traveling wave, the bifurcation of solutions with varying f is considered, the velocity of the wave has been computed as a function of γ and f. A method is proposed for integration of solitary wave (or kink) equation in the case of polynomial ''on site'' potential. At γ=0 the asymptotic stability is considered for the kinks obtained