DYNAMICS OF COUPLED TOPOLOGICAL SOLITONS IN A WEAKLY COUPLED DISCRETE SINE-GORDON SYSTEM WITH LOCAL IMPURITIES

We study the dynamics of kinks and/or antikinks in two weakly coupled discrete sine-Gordon chains with local impurities. We use the Lagrangian formalism to derive the effective equations of motion for the soliton coordinates, which takes into account the inhomogeneities, the discreteness of the lattice and the coupling between chains. It appears that the repulsive or the attractive character of the impurities depends on the soliton polarities and on competition between the impurities related to the elastic constants, the substrate potential barriers and the coupling between the chains. Conditions for the reflection and the attraction of low-velocity kink-kink, kink-antikink and antikink-antikink pairs are obtained and the threshold velocities for soliton reflection by impurities are derived.