Employing multiple scales method combined with a quasidiscreteness approximation, we investigate the wave motive equation in a one-dimensional homogeneous lattice chain with second-nearest neighbors interaction, and get a new linear dispers ion relation. The result shows that, taking into consideration the second neares t-neighbor interaction and quartic anharmonic interaction simultaneously, the on e-dimensional homogeneous lattice exhibits not only envelope soliton, kink and a ntikink, but also another non-linear elementary excitation in solitary wave form -the breather.
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