Many-fluxon kinetics in an inhomogeneous damped dc driven Josephson junction

Evolution of a Sine-Gordon Breather under the Action of Conservative Perturbations

“…(') The expression (7) is valid, provided IE/ << C. In the case (3) the expression for W is significantly different from (10) [lll: (13) (while the radiation wave number is, as above, k = k Zfl), and the breather amplitude evolves as ,U = const/(c2 t)1'5 (14) (here we assume only ~' t >> 1, but not log(E2t) >> 1). As one sees from (14) and 9, the condition A <<,U again holds.…”

“…In conclusion it is pertinent to note that a physically important conservative perturbation with which describes a uniformly distributed bias current in a long Josephson junction [41, results in the qualitative results analogous to those obtained above for the perturbation (2). Indeed, following the consideration developed for the perturbation (2) in [12,13], it is easy to obtain for the power of the LFB emission generated by the perturbation (18) the same estimate W-C (cf. (7)).…”

“…Let us start our consideration from the case of LFB. To evaluate the rate of the perturbation-induced energy emission from it, we will employ the trick used previously in [13]: in the limit <-+ 0 the LFB wave form (6) goes over into the well-known exact solution of the unperturbed SGE which describes a kink-antikink paifwith the zero velocity at infinity (see, e.g., [l]). Thus, in the lowest approximation in the small parameter <, the energy A E emitted by LFB during a half-period d C of its internal oscillations coincides with the total energy emitted by the kinkantikink pair described by the solution ukE.…”