In the series of works [24, 29,30, 35,37, P5,P7] the phase locking problem of fluxons in long Josephson junctions has been considered. In particular, in [24,30] the theory of phase locking has been developed for junctions of inline and overlap geometry. It was shown that in both cases the phenomenon of phase locking can be reduced to the study of a two dimensional map for the time of flight and for the velocity of the fluxons inside the junction. This result allowed to account for all the experimental facts known on the phenomenon as well as to predict new effects. In the works [29, 41], the existence of chaotic phenomena in long Josephson junctions induced by the phase locking dynamics was predicted. The developed theory of phase locking was also confirmed by a direct comparison with direct simulations on the sine-Gordon system, as reported in the works [55,P7]. In the group of papers [35,45, 53] the problem of chaos suppression in Josephson junctions by means of external periodic signals was considered. In particular in [35] it was shown that the addition of a small sub-harmonic component to the rf signal allows to stabilize the phase locking dynamics and suppress the deterministic chaos in the middle of the rf induced steps in the current-voltage (I-V) characteristic. As remarked at the end of work [35], and demonstrated in [45] for a PDE system, the approach to "chaos suppression" by means of periodic signals is of more general validity with respect to the context in which has been derived (can be applied to all systems which exhibit a transition to chaos via period doubling). This idea was independently and simultaneously introduced also by Braiman and Goldhirsch in Ref. Phys.Rev.Lett. 66, 2545 (1991). In the paper [46] the existence of localized soliton solutions on top of rotating backgrounds induced by external magnetic fields was proved. In particular, it was demonstrated that such solutions can exist only if the background is phase-locked to the external field. In the work [63] the phase locking of fluxons in presence of spatial inhomogeneities was considered and an analytical expression for the locking range in current as a function of the parameters of the system was derived.
In the set of papers [69, 71,72], [C2] the theory of the Josephson flux flow oscillator was developed. In the paper [69] an analytical expression for the I-V characteristic of the flux-flow oscillator was derived and shown to be in good agreement both with real experiments and with numerical simulations. The theory has been generalized to the case of external microwave fields applied to the junction both uniformly [71] and non uniformly [72]. As an interesting result it was shown that the satellite steps around the main flux-flow resonance in the I-V characteristic of the oscillator are spaced differently depending on the type of coupling realized. In particular, for microwave fields applied uniformly to the junction, the steps are spaced by multiples of the external frequency while in case of nonuniform rf fields (applied at the edges of the junction) they are spaced only by even multiples of the external frequency. This theoretical prediction were recently confirmed by real experiments.