Domain-wall-like excitations in a discrete one-dimensional anharmonic lattice model

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Abstract
In the discrete chain of harmonically coupled particles moving in double-minimum potential wells (the discrete Phi 4 model), static and dynamical domain-wall-type solutions are studied. In the static case, no translationally invariant solutions exist, but rather two special discrete-ones. The energy difference between the two determines the pinning of the domain wall to a lattice site and is shown to be exponentially small for larger coupling parameters. The authors also present a non-trivial dynamical permanent profile solution, which corresponds to the propagating domain wall with a vanishing average velocity.