Symmetry-breaking bifurcations and ghost states in the fractional nonlinear Schrödinger equation with a PT-symmetric potential.

  title={Symmetry-breaking bifurcations and ghost states in the fractional nonlinear Schr{\"o}dinger equation with a PT-symmetric potential.},
  author={Pengfei Li and Boris A. Malomed and Dumitru Mihalache},
  journal={Optics letters},
  volume={46 13},
We report symmetry-breaking and restoring bifurcations of solitons in a fractional Schrödinger equation with cubic or cubic-quintic (CQ) nonlinearity and a parity-time-symmetric potential, which may be realized in optical cavities. Solitons are destabilized at the bifurcation point, and, in the case of CQ nonlinearity, the stability is restored by an inverse bifurcation. Two mutually conjugate branches of ghost states (GSs), with complex propagation constants, are created by the bifurcation… 

Figures from this paper

Symmetry-breaking transitions in quiescent and moving solitons in fractional couplers

We consider phase transitions, in the form of spontaneous symmetry breaking (SSB) bifurcations of solitons, in dual-core couplers with fractional diffraction and cubic self-focusing acting in each

Spontaneous symmetry breaking and ghost states supported by the fractional nonlinear Schr\"odinger equation with focusing saturable nonlinearity and PT-symmetric potential

We report a novel spontaneous symmetry breaking phenomenon and ghost states existed in the framework of the fractional nonlinear Schr\"odinger (FNLS) equation with focusing saturable nonlinearity and

Asymmetric localized states at a nonlinear interface of fractional systems with optical lattices

We investigate the existence and stability of localized gap states at a non-linear interface of non-linear fractional systems in a one-dimensional photonic lattice. By using the direct numerical

Optical Solitons and Vortices in Fractional Media: A Mini-Review of Recent Results

The article produces a brief review of some recent results which predict stable propagation of solitons and solitary vortices in models based on the nonlinear Schrodinger equation (NLSE) including

Nondegenerate solitons in the integrable fractional coupled Hirota equation

Wave transport in fractional Schrodinger equations

In this paper, we have investigated the localization of an input spatial soliton as it propagates through a system where can be described by a fractional Schrodinger equation. In order to solve the

Fractional Integrable Nonlinear Soliton Equations.

Nonlinear integrable equations serve as a foundation for nonlinear dynamics, and fractional equations are well known in anomalous diffusion. We connect these two fields by presenting the discovery of

One-dimensional PT -symmetric eigenmodes in k-wave number Scarf II potential with defocusing nonlinearity

The stationary states and dynamical evolution of one-dimensional eigenmodes in self-defocusing nonlinear Kerr medium under transverse parity-time (  ) symmetric k-wave number Scarff-II potential

Inverse scattering transform for the integrable fractional derivative nonlinear Schr\"odinger equation

In this paper, we explore the integrable fractional derivative nonlinear Schr\"odinger (fDNLS) equation by using the inverse scattering transform. Firstly, we start from the recursion operator and

Snakes and ghosts in a parity-time-symmetric chain of dimers.

It is shown that ghost localized states associated with growth or decay also exhibit snaking bifurcation diagrams, and asymptotic approximations in the limit of strong and weak coupling where good agreement is obtained are provided.

Symmetry breaking of solitons in two-dimensional complex potentials.

  • Jianke Yang
  • Physics, Mathematics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2015
One is that at the bifurcation point, zero and simple imaginary linear-stability eigenvalues of asymmetric solitons can move directly into the complex plane and create oscillatory instability, and the other is that the two bIfurcated asymmetricsolitons, even though having identical powers, can possess different types of unstable eigen values and thus exhibit nonreciprocal nonlinear evolutions under random-noise perturbations.

Symmetry breaking and restoration of symmetric solitons in partially parity-time-symmetric potentials

We address the symmetry-breaking bifurcation of optical solitons in cubic–quintic media with an imprinted partially parity-time-symmetric potential. An increase in soliton power leads to symmetry

Symmetry breaking of solitons in one-dimensional parity-time-symmetric optical potentials.

In a special class of PT-symmetric potentials V(x)=g(2)(x)+αg(x)+ig'(x), where g(x) is a real and even function and α a real constant, symmetry breaking of solitons can occur.

One-dimensional solitons in fractional Schrödinger equation with a spatially periodical modulated nonlinearity: nonlinear lattice

The existence and stability of stable bright solitons in one-dimensional (1D) fractional media with a spatially periodical modulated Kerr nonlinearity (nonlinear lattice), supported by the recently

Optical solitons, self-focusing, and wave collapse in a space-fractional Schrödinger equation with a Kerr-type nonlinearity.

The nonlinear dynamics of (1+1)-dimensional optical beam in the system described by the space-fractional Schrödinger equation with the Kerr nonlinearity is investigated and a physical explanation for the collapse is given.

Double Loops and Pitchfork Symmetry Breaking Bifurcations of Optical Solitons in Nonlinear Fractional Schrödinger Equation with Competing Cubic‐Quintic Nonlinearities

Symmetry breaking bifurcations of solitons are investigated in framework of a nonlinear fractional Schrödinger equation (NLFSE) with competing cubic‐quintic nonlinearity. Some prototypical

Nonlocal solitons in fractional dimensions.

It is revealed that multipole-mode solitons, including an arbitrary number of peaks, can propagate stably in fractional systems provided that the propagation constant exceeds a certain value, which is in sharp contrast to conventional nonlocal systems under a normal diffraction, where bound states composed of five peaks or more are completely unstable.