We study analytically and numerically a one-dimensional atomic chain with a new type of nonlinear periodic substrate potential $V(\phi , r)$ whose shape can be varied continuously as a function of parameter $r$ and which has the sine-Gordon potential as a particular case. In the continuum limit the equation of motion admits two classes of solitary wave (kink) solutions which are calculated exactly. As the shape parameter $r$ is increased in the range $-1<r<\mathrm{}1\mathrm{}$ the spatial extension of the kinks increases and their energy decreases. Numerical simulations show that the kinks are transparent to small-amplitude solutions. Moreover kink-kink and kink-antikink collisions show that kinks behave like quasisolitons. Breather modes are also observed. Owing to their importance in many physical problems (dislocations, domain walls, etc.) discreteness effects are investigated in details. They are strongly dependent on the shape of the substrate potential: When it becomes sharp even very large kinks may be pinned by the lattice. Calculations of the pinning (Peierls) barrier and shape of the pinning potential are performed. Minima of the Peierls barrier are obtained when $r$ approaches -1. From our results it appears that the shape of the substrate potential is a factor of particular importance when modeling physical systems.

• Received 27 April 1982

DOI:https://doi.org/10.1103/PhysRevB.26.2886