Considering the second nearest-neighbor interaction and cubic,quartic anharmonic interactions simultaneously, we employ the multiple scales method combined with a quasidiscreteness approximation to calculate the lattice vibration.It is shown that the kind of nonlinear chain exhibits envelope soliton,envelope kink and envelope antikink soliton.These results can also be used to explain the experimental phenomena that the kink amplitude of the self-localized structure is determined only by the intrinsic properties of its lattices.