Soliton dynamics in new models with parametrized periodic double-well and asymmetric substrate potentials

Abstract

A chain of atoms, harmonically coupled, subjected to a new type of parametrized substrate potential is studied in the strong coupling limit. We consider in particular two cases in which the shape of the potential can be moved in a controlled manner from the simply periodic and symmetrical sine-Gordon model to doubly periodic potentials: a periodic double-well deformable potential (DWDP) and an asymmetrical deformable potential (ASDP). Kinks solutions are calculated analytically in the continuum limit. In the DWDP case two types of symmetric kinks with different masses are obtained. In this model the numerical studies of kink-kink and kink-antikink collisions show that kinks properties are very close to those of an integrable system. Consequently, the collisions are well described by treating the excitations as relativistic quasiparticles if conversion between the two types of particles is taken into account. In the ASDP case, two types of asymmetric kinks with identical masses are found. Owing to this asymmetry, the interaction between two excitations depends on the side of the kinks which first comes into contact during the collision, and this ''polarization'' of the kinks introduces new features when they collide. Moreover, these kinks interpolate between two ground states which do not havemore » the same phonon spectrum. In some cases small-amplitude oscillations can be trapped between a kink and an antikink and induce a new type of resonant interaction between them. In addition, in the search for breather solutions as the low-amplitude limit of nonlinear Schroedinger envelope solitons, necessary conditions for the existence of breather modes are determined analytically and confirmed numerically.« less