For the first time, the possibility of existence of topological solitons in one-component chain with a non-degenerate potential of gradient type is proven. The existence and stability of the solitons is ensured by competing piecewise-parabolic nearest-neighbor and parabolic second-nearest-neighbor interactions. The solitons are shown to move at a unique velocity. Soliton propagation may constitute an elementary event of structural transformations in the chain.

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