Multisoliton Newton's cradles and supersolitons in regular and parity-time-symmetric nonlinear couplers

Symmetric and asymmetric solitons supported by a 𝒫𝒯-symmetric potential with saturable nonlinearity: bifurcation, stability and dynamics

The symmetry breaking bifurcation of solitons in an optical waveguide with focusing saturable nonlinearity and parity-time (𝒫𝒯)-symmetric complex-valued external potentials is investigated. As the soliton power increases, it is found that the branches of asymmetric solitons split off from the base branches of 𝒫𝒯-symmetric fundamental soliton. The bifurcation diagrams, consisting essentially of the propagation constants of optical solitons, indicate that symmetric fundamental and multipole solitons, as well as asymmetric solitons can exist. The stabilities and the dynamics characteristics of solitons are comprehensively investigated. We find the different instability scenarios of the symmetric solitons, but the symmetry breaking bifurcation is caused only by the onset of instability of the symmetric fundamental solitons. This result is further confirmed by the numerical examples with the different saturable nonlinearity parameters. In particular, we find that the soliton power and the stability of soliton at the bifurcation points are significantly changed by varying the strength of the saturable nonlinearities. These results provide additional way to control symmetry breaking bifurcations in 𝒫𝒯-symmetric optical waveguide.

PT-symmetric couplers with competing cubic-quintic nonlinearities

We introduce a one-dimensional model of the parity-time ( PT)-symmetric coupler, with mutually balanced linear gain and loss acting in the two cores, and nonlinearity represented by the combination of self-focusing cubic and defocusing quintic terms in each core. The system may be realized in optical waveguides, in the spatial and temporal domains alike. Stationary solutions for PT-symmetric solitons in the systems are tantamount to their counterparts in the ordinary coupler with the cubic-quintic nonlinearity, where the spontaneous symmetry breaking of solitons is accounted for by bifurcation loops. A novel problem is stability of the PT-symmetric solitons, which is affected by the competition of the PT symmetry, linear coupling, cubic self-focusing, and quintic defocusing. As a result, the solitons become unstable against symmetry breaking with the increase of the energy (alias integral power, in terms of the spatial-domain realization), and they retrieve the stability at still larger energies. Above a certain value of the strength of the quintic self-defocusing, the PT symmetry of the solitons becomes unbreakable. In the same system, PT-antisymmetric solitons are entirely unstable. We identify basic scenarios of the evolution of unstable solitons, which may lead to generation of additional ones, while stronger instability creates expanding quasi-turbulent patterns with limited amplitudes. Collisions between stable solitons are demonstrated to be quasi-elastic.

Solitons riding on solitons and the quantum Newton's cradle

The reduced dynamics for dark and bright soliton chains in the one-dimensional nonlinear Schrödinger equation is used to study the behavior of collective compression waves corresponding to Toda lattice solitons. We coin the term hypersoliton to describe such solitary waves riding on a chain of solitons. It is observed that in the case of dark soliton chains, the formulated reduction dynamics provides an accurate an robust evolution of traveling hypersolitons. As an application to Bose-Einstein condensates trapped in a standard harmonic potential, we study the case of a finite dark soliton chain confined at the center of the trap. When the central chain is hit by a dark soliton, the energy is transferred through the chain as a hypersoliton that, in turn, ejects a dark soliton on the other end of the chain that, as it returns from its excursion up the trap, hits the central chain repeating the process. This periodic evolution is an analog of the classical Newton's cradle.

Breatherlike solitons extracted from the Peregrine rogue wave

Based on the Peregrine solution (PS) of the nonlinear Schrödinger (NLS) equation, the evolution of rational fraction pulses surrounded by zero background is investigated. These pulses display the behavior of a breatherlike solitons. We study the generation and evolution of such solitons extracted, by means of the spectral-filtering method, from the PS in the model of the optical fiber with realistic values of coefficients accounting for the anomalous dispersion, Kerr nonlinearity, and higher-order effects. The results demonstrate that the breathing solitons stably propagate in the fibers. Their robustness against small random perturbations applied to the initial background is demonstrated too.