Pinning-free soliton lattices and bifurcation in a discrete double-well model: exact results

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Abstract
It is shown that the chain of coupled particles in the double-well potential introduced by Schmidt (1979) is completely integrable in the static limit. The chaotic behaviour and the associated infinite series of bifurcations found in the related discrete phi 4 theory are absent in the model. The solutions are generally unpinned soliton lattices. The model exhibits a bifurcation where a hyperbolic fixed point becomes elliptic and splits into two hyperbolic fixed points. The bifurcation does not lead to chaos.