Using the exact breather lattice solution of the sine-Gordon equation, we obtain the asymptotic interaction between two breathers. We identify the exponential dependence of the interaction on the breather separation as well as its power-law dependence on the breather frequency. Numerical simulation of the breather lattice demonstrates its instability. However, stabilization of such structures is found to be feasible through ac driving and damping. Finally, other limits of the original periodic solution are traced, obtaining the leading-order terms in the interaction between “pseudosphere” solutions and kink-antikink pairs.

• Received 7 April 2001

DOI:https://doi.org/10.1103/PhysRevE.64.026613