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This paper studies the evolution of wave in the system of a pure anharmonic lattice with a double well on-site potential by numerical calculation. It finds that an initial distribution of static or moving wave can evolve into two travelling soliton-like trains with contrary directions and a region of oscillation in this lattice system. It presents that some cases with cosine-square-shape and Gaussian-shape initial distribution of static or moving wave will produce ordered soliton-like train. Careful numerical observation shows that the centre oscillation region in this system may act as a resource of generating soliton-like train.