Peregrine rogue waves in the nonlocal nonlinear Schrödinger equation with parity-time symmetric self-induced potential
arXiv:1710.08624 · doi:10.1016/j.optcom.2017.10.055
Abstract
In this work, based on the recently proposed (Phys. Rev. Lett. 110 (2013) 064105) continuous nonlocal nonlinear Schrödinger system with parity-time symmetric Kerr nonlinearity (PTNLSE), a numerical investigation has been carried out for two first order Peregrine solitons as the initial ansatz. Peregrine soliton, as an exact solution to the PTNLSE, evokes a very potent question: what effects does the interaction of two first order Peregrine solitons have on the overall optical field dynamics. Upon numerical computation, we observe the appearance of Kuznetsov-Ma (KM) soliton trains in the unbroken PT-phase when the initial Peregrine solitons are in phase. In the out of phase condition, it shows repulsive nonlinear waves. Quite interestingly, our study shows that within a specific range of the interval factor in the transverse coordinate there exists a string of high intensity well-localized Peregrine rogue waves in the PT unbroken phase. We note that the interval factor as well as the transverse shift parameter play important roles in the nonlinear interaction and evolution dynamics of the optical fields. This could be important in developing fundamental understanding of nonlocal non-Hermitian NLSE systems and dynamic wave localization behaviors.
arXiv comment9 pages, 7 Figures; To appear in Opt. Commun
References in corpus (34)
- Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
- PT-symmetry breaking and laser-absorber modes in optical scattering systems
- PT-symmetric laser-absorber
- Unidirectional Nonlinear PT-symmetric Optical Structures
- Modulation instability, Akhmediev Breathers and continuous wave supercontinuum generation
- Pump-induced Exceptional Points in Lasers
- PT-symmetry in honeycomb photonic lattices
- Stability of solitons in PT-symmetric couplers
- Nonlinear suppression of time-reversals in PT-symmetric optical couplers
- Optical solitons in -symmetric nonlinear couplers with gain and loss
- Observation of Defect States in PT-Symmetric Optical Lattices
- Continuous and discrete Schrodinger systems with PT-symmetric nonlinearities
- Dynamics of higher-order rational solitons for the nonlocal nonlinear Schrodinger equation with the self-induced parity-time-symmetric potential
- PT-Symmetric Oligomers: Analytical Solutions, Linear Stability and Nonlinear Dynamics
- PT-Symmetric Sinusoidal Optical Lattices at the Symmetry-Breaking Threshold
- Periodic and Hyperbolic Soliton Solutions of a Number of Nonlocal PT-Symmetric Nonlinear Equations
- Supersymmetry-generated complex optical potentials with real spectra
- Stable dark solitons in PT-symmetric dual-core waveguides
- Optical mesh lattices with PT-symmetry
- Bragg solitons in nonlinear PT-symmetric periodic potentials
- Solitons in a chain of PT-invariant dimers
- Rational Solitons in the Parity-Time-Symmetric Nonlocal Nonlinear Schrödinger Model
- A note on the PT-invariant periodic potential V(x)=4 cos^2 x + 4 i V_0 sin 2x
- Linear and Nonlinear PT-symmetric Oligomers: A Dynamical Systems Analysis
- On Symmetries and Exact Solutions of a Class of Non-local Non-linear Schrodinger Equations with Self-induced PT-symmetric Potential
- Bloch oscillations in complex crystals with PT symmetry
- Breather-like solitons extracted from the Peregrine rogue wave
- Origin of maximal symmetry breaking in even PT-symmetric lattices
- Peregrine Rogue Wave dynamics in the continuous nonlinear Schrödinger system with parity-time symmetric Kerr nonlinearity
- Self-organization, Pattern Formation, Cavity Solitons and Rogue Waves in Singly Resonant Optical Parametric Oscillators
- Fluctuating and dissipative dynamics of dark solitons in quasi-condensates
- Collisional Dynamics of Solitons in the Coupled PT symmetric Nonlocal nonlinear Schrodinger equations
- Quasiperiodic oscillations and homoclinic orbits in the nonlinear nonlocal Schrödinger equation
- Solitary waves in Parity-time (PT) symmetric Bragg-grating structure and the existence of Optical Rogue Waves