Abstract
The authors study the effects of discreteness on the motion of coupled solitons of two weakly coupled discrete sine-Gordon systems. A collective coordinate method associated with Dirac's formalism of constrained Hamiltonian dynamics is used to derive the equations of motion for the centres of the solitons and for the dressing or discreteness corrections of the continuum solitons. The authors show that the dynamics of the coupled solitons can be described by a set of two non-linear differential equations. It is also shown that the coupling reduces (increases) the trapping processes in the case where the two solitons have the same polarity (different polarities). A numerical analysis of the static dressing equations is performed. They find that the dressing lowers the potential energy of solitons and increases the Peierls-Nabarro barrier.
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