ONE-COLLECTIVE AND 2-COLLECTIVE VARIABLE DESCRIPTIONS OF 2 INTERACTING SINE-GORDON KINKS

Using an ansatz [T. Matsuda, Lett. Nuovo Cimento 24 (1979) 207] which is an exact collective variable (CV) solution for kink-kink (K-K) and kink-antikink (K-A) interactions as well as for the breather in the un perturbed sine-Gordon (SG) equation and uses only one CV r(t), the sep aration between the kinks, we study the effects of microshort and micr oresistor perturbations in a Josephson junction transmission line on K -K interactions. Representing the energy stored in microshorts and mic roresistors, these perturbations can profoundly alter the motion of fl uxons, which we term kinks, in Josephson junction transmission lines. With this ansatz, we describe particle characteristics, including rela tivistic effects, of K-K and K-A interactions and the breather in the unperturbed SG system. Because, in a perturbed SG system, this ansatz is no longer exact, we modify it by treating the slope of the kinks Ga mma(t) as a CV. We derive the masses of the r and Gamma CVs, the inter action potentials, and the Hamiltonians for K-K and K-A. The inclusion of Gamma(t) qualitatively and quantitatively changes the results of t he one-CV r(t) description. Significantly, moderately strong microshor t (microresistor) perturbations and highly relativistic initial veloci ties increase (decrease) the time advance tau, defined as delta/nu, wh ere nu is the single kink velocity and delta is the kinks' increased s eparation or phase shift due to their interaction, in two-CV K-K scatt ering relative to the unperturbed tau, by almost a factor of two for t he microshort, whereas these conditions produce the reverse qualitativ e and a smaller quantitative effect on the one-CV K-K tau. In contrast , for weaker perturbations and slower initial velocities, a microshort (microresistor) decreases (increases) the tau compared to the unpertu rbed tau for both the one- and two-CV descriptions. (C) 1998 Elsevier Science B.V.