Oscillations of a highly discrete breather with a critical regime

Strong-chaos-caused negative mobility in a periodic substrate potential

We numerically investigate negative mobility of an inertial Brownian particle moving in a periodic double-well substrate potential in the presence of a time-periodic force and a constant bias. For the deterministic case, we find from the average velocity that the varying shape parameter and driving forces can cause negative mobility, differential negative mobility, and giant positive mobility. We analyze these findings via the bifurcation diagram and maximal Lyapunov exponent and find that certain chaos can give rise to negative mobility. For the presence of a Gaussian color noise, the results suggest that the noise intensity can enhance or result in negative and positive mobilities, whereas correlation time can enhance, weaken, or even eliminate them. On the basis of the time series, phase-space map, and power spectrum of various attractors, we unveil how these mobilities connect to strong chaotic attractors (SCAs), including both stable attractor and unstable attractors, and propose an underlying mechanism that SCAs can result in the negative mobility, whereas other attractors do not. Our findings may be potentially useful for research on anomalous transports of the particles and on designs of various devices, such as atomic chains, crystals with dislocations, and superconducting nanowires, etc.

Conservative and PT-symmetric compactons in waveguide networks

Stable discrete compactons in interconnected three-line waveguide arrays are found in linear and nonlinear limits in conservative and in parity-time (PT)-symmetric models. The compactons result from the interference of the fields in the two lines of waveguides ensuring that the third (middle) line caries no energy. PT-symmetric compactons require not only the presence of gain and losses in the two lines of the waveguides but also complex coupling, i.e., gain and losses in the coupling between the lines carrying the energy and the third line with zero field. The obtained compactons can be stable and their branches can cross the branches of the dissipative solitons. Unusual bifurcations of branches of solitons from linear compactons are described.

Bright compact breathers

In this communication we will consider the potential of some general classes of nonlinear lattice models to support bright discrete compact breather solutions (compactlets). We analyze the conditions for which such solutions are possible and classify the models as belonging in three general categories: a class with no compact breather solutions, one with one-parameter families of solutions, and a class with "isolated" solutions (i.e., no free parameters). In the latter two cases we construct the solutions and analyze their linear stability. The drastically different stability features of these solutions in comparison with their smoothly decaying counterparts are discussed. Stable breather solutions with compact support are identified in the one-parameter families of solutions, while the corresponding solutions found in the zero-parameter families are always found to be unstable.

Orientational discrete breathers in hydrogen-bonded chains

We consider rotational motion of protons within a hydrogen-bonded zig-zag chain. Each proton is subjected to a Coulomb interaction from the three nearest heavy ions, as well as from the two neighboring protons. The hydrogen bonding is modeled with an additional double-minimum on-site potential. The system admits discrete breather solutions in the gap below the phonon band. The numerically exact procedure using an anticontinuum limit is exploited to obtain these solutions, which appear to be asymmetric due to the asymmetry of the interaction potential. Only single-well orbits are considered. A linear stability analysis is performed. The discrete breather solutions are shown to be linearly stable provided the nonresonance condition is satisfied, and they turn out to be unstable in the region of 2:3 parametric resonance. Phonon-breather solutions are found in the 1:2 resonance region. Two kinds of two-site breather solutions are investigated.