We propose a system which can generate a periodic array of solitary-wave pulses from a finite reservoir of coherent Bose-Einstein condensate (BEC). The system is built as a set of two parallel quasi-one-dimensional traps (the reservoir proper and a pulse-generating cavity), which are linearly coupled by the tunneling of atoms. The scattering length is tuned to be negative and small in the absolute value in the cavity, and still smaller but positive in the reservoir. Additionally, a parabolic potential profile is created around the center of the cavity. Both edges of the reservoir and one edge of the cavity are impenetrable. Solitons are released through the other cavity's edge, which is semitransparent. Two different regimes of the intrinsic operation of the laser are identified: circulations of a narrow wave-function pulse in the cavity, and oscillations of a broad standing pulse. The latter regime is stable, readily providing for the generation of an array containing up to 10, 000 permanentshape pulses. The circulation regime provides for no more than 40 cycles, and then it transforms into the oscillation mode. The dependence of the dynamical regime on parameters of the system is investigated in detail.

We study collisions of moving solitons in a fiber Bragg grating with a structure composed of two local defects of the grating, attractive or repulsive. Results are summarized in the form of diagrams showing the share of the trapped energy as a function of the soliton's velocity and defects' strength. The moving soliton can be trapped by a cavity bounded by repulsive defects; a well-defined region of the most efficient trapping is identified. The trapped soliton performs persistent oscillations in the cavity, with the frequency in the GHz range. For attractive defects, essential differences are found from the earlier studied case of the collision of a soliton with a single defect: in this case, too, there appears a well-defined region of the most efficient trapping, and the largest velocity, up to which the soliton can be captured, increases. The findings may be significant for experiments aimed at the creation of "standing-light" pulses in the fiber gratings and for related applications. Collisions between identical solitons moving across the two-defect structure are also studied. On the attractive set, soliton-soliton collisions may give rise to symmetric capture of the solitons by both defects or merger into a single pulse trapped at one defect.

Squeeze film dampers introduce nonlinear motion dependent damper forces into otherwise linear rotor bearing systems, thereby considerably complicating their analysis. Noncircular orbit type dampers, such as unsupported or uncentralized dampers, have generally necessitated transient solutions, which are computationally prohibitive for design studies of large order systems, particularly for systems with low damping. By utilizing harmonic balance with appropriate condensation, it is possible to considerably reduce the number of simultaneous nonlinear equations inherent to this approach. The stability (linear) of the equilibrium solutions may be conveniently evaluated using Floquet theory, particularly if the damper force components are evaluated in fixed, rather than rotating, reference frames. The versatility of this technique is illustrated on systems of increasing complexity with and without damper centralizing springs. Of particular interest, is its applicability to unsupported systems illustrating how such systems can lift off and, with further increase in speed, the damper forces can be linearized about the orbit center.

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The problem of the stability of solitons in second-harmonic-generating media with normal group-velocity dispersion (GVD) in the second-harmonic (SH) field, which is generic to available χ (2) materials, is revisited. Using an iterative numerical scheme to construct stationary soliton solutions, and direct simulations to test their stability, we identify a full soliton-stability range in the space of the system's parameters, including the coefficient of the group-velocity-mismatch (GVM). The soliton stability is limited by an abrupt onset of growth of tails in the SH component, the relevant stability region being defined as that in which the energy loss to the tail generation is negligible under experimentally relevant conditions. We demonstrate that the stability domain can be readily expanded with the help of two "management" techniques (spatially periodic compensation of destabilizing effects) -the dispersion management (DM) and GVM management. In comparison with their counterparts in optical fibers, DM solitons in the χ (2) medium feature very weak intrinsic oscillations.