Interactions of bright and dark solitons with localized PT-symmetric potentials

Unidirectional segregation of bright-bright soliton through a parity-time-symmetric potential

We study the dynamics of two-component vector solitons, namely, bright-bright (BB) solitons interacting with parity-time (PT)-symmetric potentials. We employ direct numerical simulations to demonstrate the unidirectional segregation of the BB soliton. Using a modified perturbed dynamical variational Lagrangian approximation, we develop an analytical model to verify the results obtained from numerical calculations. Simplified variational equations of motion suggest that the splitting of BB solitons can be explained by considering the effective force between the two components.

Stable flat-top solitons and peakons in the PT-symmetric δ-signum potentials and nonlinear media

We discover that the physically interesting PT-symmetric Dirac delta-function potentials can not only make sure that the non-Hermitian Hamiltonians admit fully-real linear spectra but also support stable peakons (nonlinear modes) in the Kerr nonlinear Schrödinger equation. For a specific form of the delta-function PT-symmetric potentials, the nonlinear model investigated in this paper is exactly solvable. However, for a class of PT-symmetric signum-function double-well potentials, a novel type of exact flat-top bright solitons can exist stably within a broad range of potential parameters. Intriguingly, the flat-top solitons can be characterized by the finite-order differentiable waveforms and admit the novel features differing from the usual solitons. The excitation features and the direction of transverse power flow of flat-top bright solitons are also explored in detail. These results are useful for the related experimental designs and applications in nonlinear optics and other related fields.

Attraction centers and parity-time-symmetric delta-functional dipoles in critical and supercritical self-focusing media

We introduce a model based on the one-dimensional nonlinear Schrödinger equation with critical (quintic) or supercritical self-focusing nonlinearity. We demonstrate that a family of solitons, which are unstable in this setting against the critical or supercritical collapse, is stabilized by pinning to an attractive defect, that may also include a parity-time (PT)-symmetric gain-loss component. The model can be realized as a planar waveguide in nonlinear optics, and in a super-Tonks-Girardeau bosonic gas. For the attractive defect with the delta-functional profile, a full family of the pinned solitons is found in an exact analytical form. In the absence of the gain-loss term, the solitons' stability is investigated in an analytical form too, by means of the Vakhitov-Kolokolov criterion; in the presence of the PT-balanced gain and loss, the stability is explored by means of numerical methods. In particular, the entire family of pinned solitons is stable in the quintic (critical) medium if the gain-loss term is absent. A stability region for the pinned solitons persists in the model with an arbitrarily high power of the self-focusing nonlinearity. A weak gain-loss component gives rise to intricate alternations of stability and instability in the system's parameter plane. Those solitons which are unstable under the action of the supercritical self-attraction are destroyed by the collapse. On the other hand, if the self-attraction-driven instability is weak and the gain-loss term is present, unstable solitons spontaneously transform into localized breathers, while the collapse does not occur. The same outcome may be caused by a combination of the critical nonlinearity with the gain and loss. Instability of the solitons is also possible when the PT-symmetric gain-loss term is added to the subcritical nonlinearity. The system with self-repulsive nonlinearity is briefly considered too, producing completely stable families of pinned localized states.