Solitons in PT-symmetric nonlinear lattices

Abstract

Existence of localized modes supported by the PT-symmetric nonlinear lattices is reported. The system considered reveals unusual properties: unlike other typical dissipative systems it possesses families (branches) of solutions, which can be parametrized by the propagation constant; relatively narrow localized modes appear to be stable, even when the conservative nonlinear lattice potential is absent; finally, the system supports stable multipole solutions.

References in corpus (3)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Solitons in nonlinear lattices
• Dissipative periodic waves, solitons and breathers of the nonlinear Schrodinger equation with complex potentials

Cited by in corpus (108)

• Non-Hermitian Physics
• Nonlinear waves in $\mathcal{P}\mathcal{T}$-symmetric systems
• Nonlinear switching and solitons in PT-symmetric photonic systems
• Observation of Parity-Time Symmetry in Optically Induced Atomic Lattices
• Observation of Asymmetric Transport in Structures with Active Nonlinearities
• Stability analysis for solitons in PT-symmetric optical lattices
• Stability of solitons in PT-symmetric couplers
• Model of a PT symmetric Bose-Einstein condensate in a delta-functions double well
• Nonlinearly-PT-symmetric systems: spontaneous symmetry breaking and transmission resonances
• Dark solitons and vortices in PT-symmetric nonlinear media: from spontaneous symmetry breaking to nonlinear PT phase transitions
• Nonlinear modes in finite-dimensional PT-symmetric systems
• PT-Symmetric Oligomers: Analytical Solutions, Linear Stability and Nonlinear Dynamics
• Nonlinear modes in the harmonic PT-symmetric potential
• Breathers in PT-symmetric optical couplers
• 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
• Nonlinear localized modes in PT-symmetric Rosen-Morse potential well
• Spatial solitons and stability in self-focusing and defocusing Kerr nonlinear media with generalized PT-symmetric Scarff-II potentials
• Stability boundaries and collisions of two-dimensional solitons in PT-symmetric couplers with the cubic-quintic nonlinearity
• Symmetry breaking of solitons in one-dimensional parity-time-symmetric optical potentials
• Partially-PT-symmetric optical potentials with all-real spectra and soliton families in multi-dimensions
• Stability of localized modes in PT-symmetric nonlinear potentials
• Families of fundamental and multipole solitons in a cubic-quintic nonlinear lattice in fractional dimension
• Stabilization of solitons in PT models with supersymmetry by periodic management
• Stable localized modes in asymmetric waveguides with gain and loss
• Vector solitons in PT-symmetric lattices
• Families of stationary modes in complex potentials
• Nonlinear Schrödinger equation for a PT symmetric delta-functions double well
• Discrete solitons in PT-symmetric lattices
• Parity-time-symmetric optical lattice with alternating gain and loss atomic configurations
• Integrable nonlocal Hirota equations
• Unbreakable PT-symmetry of solitons supported by inhomogeneous defocusing nonlinearity
• Theory of Exceptional Points of Degeneracy in Uniform Coupled-Waveguides and Balance of Gain and Loss
• Non-Dissipative Non-Hermitian Dynamics and Exceptional Points in Coupled Optical Parametric Oscillators
• Symmetry breaking of solitons in two-dimensional complex potentials
• Discrete solitons and vortices on two-dimensional lattices of $\mathcal{P}\mathcal{T}$-symmetric couplers
• Asymmetric Wave Propagation Through Nonlinear PT-symmetric Oligomers
• Linear and Nonlinear PT-symmetric Oligomers: A Dynamical Systems Analysis
• A solvable model for solitons pinned to a PT-symmetric dipole
• Localized modes in ${\chi }^{(2)}$ media with $\PT$-symmetric localized potential
• Nonlinear PT-symmetric plaquettes
• Solitons and their stability in the nonlocal nonlinear Schroedinger equation with PT-symmetric potentials
• Quadratic fractional solitons
• Necessity of PT symmetry for soliton families in one-dimensional complex potentials
• Decay and fragmentation in an open Bose-Hubbard chain
• On stable solitons and interactions of the generalized Gross-Pitaevskii equation with PT-and non-PT-symmetric potentials
• Solitons in $\mathcal{P}\mathcal{T}$-symmetric periodic systems with the quadratic nonlinearity
• On integrable wave interactions and Lax pairs on symmetric spaces
• PT-symmetry in optics beyond the paraxial approximation
• On the N-wave Equations with PT-symmetry
• Nonlinear localized modes in PT-symmetric optical media with competing gain and loss
• Spectral singularities in PT-symmetric Bose-Einstein condensates
• Stability of soliton families in nonlinear Schroedinger equations with non-parity-time-symmetric complex potentials
• Experimental demonstration of coherence flow in $\mathcal{P}\mathcal{T}$- and anti-$\mathcal{P}\mathcal{T}$-symmetric systems
• Interaction induced dynamical $\mathcal{P}\mathcal{T}$ symmetry breaking in dissipative Fermi-Hubbard models
• Spontaneous symmetry breaking and ghost states supported by the fractional nonlinear Schrödinger equation with focusing saturable nonlinearity and PT-symmetric potential
• Optical solitons in media with focusing and defocusing saturable nonlinearity and a parity-time-symmetric external potential
• Symmetry breaking in dipolar matter-wave solitons in dual-core couplers
• Soliton dynamics in symmetric and non-symmetric complex potentials
• Analytical stable Gaussian soliton supported by a parity-time-symmetric potential with power-law nonlinearity
• Bubbles and W-shaped solitons in Kerr media with fractional diffraction
• Discrete solitons in self-defocusing systems with $\mathcal{P}\mathcal{T}$-symmetric defects
• Defect solitons supported by nonlocal PT symmetric superlattices
• Stationary modes and integrals of motion in nonlinear lattices with PT-symmetric linear part
• Scattering properties of PT-symmetric objects
• Mode pairs in $\mathcal{P}\mathcal{T}$-symmetric multimode waveguides
• Resonant mode conversion in the waveguides with an unbroken and broken PT-symmetry
• Impact of near-PT symmetry on exciting solitons and interactions based on a complex Ginzburg-Landau model
• Interactions of bright and dark solitons with localized $\mathcal{P}\mathcal{T}$-symmetric potentials
• Bulk vortices and half-vortex surface modes in parity-time-symmetric media
• Realizing PT-symmetric BEC subsystems in closed hermitian systems
• Stable surface solitons in truncated complex potentials
• PT-symmetric lattices with spatially extended gain/loss are generically unstable
• Scattering of gap solitons by PT-symmetric defects
• Modulation theory in PT-Symmetric Magnetic Metamaterial Arrays in the continuum limit
• Continuous families of solitary waves in non-symmetric complex potentials: A Melnikov theory approach
• Nonlocal reductions of the Ablowitz-Ladik equation
• Nonlinear wave dynamics near phase transition in $\mathcal{P}\mathcal{T}$-symmetric localized potentials
• Nonlinear parity-time-symmetric transition in finite-size optical couplers
• Light propagation in periodically modulated complex waveguides
• PT-symmetry, indefinite damping and dissipation-induced instabilities
• Multisoliton Newton's cradles and supersolitons in regular and PT-symmetric nonlinear couplers
• Quasi-energies, parametric resonances, and stability limits in ac-driven $\mathcal{P}\mathcal{T}$-symmetric systems
• PT-symmetry Management in Oligomer Systems
• Edge and bulk dissipative solitons in modulated PT-symmetric waveguide arrays
• Bistable soliton switching dynamics in a $\mathcal{P}\mathcal{T}$-symmetric coupler with saturable nonlinearity
• On nonlocal reductions of the multi-component nonlinear Schrodinger equation on symmetric spaces
• PT-symmetric sine-Gordon breathers
• Loss of phase and universality of stochastic interactions between laser beams
• Asymmetric soliton mobility in competing linear-nonlinear PT-symmetric lattices
• Controllable high-speed polariton waves in a PT-symmetric lattice
• Wireless energy transfer in non-Hermitian quantum battery
• Effects of the third-order dispersion on continuous waves in complex potentials
• Stability of Bose-Einstein condensates in a $\mathcal{P}\mathcal{T}$ symmetric double-$\delta$ potential close to branch points
• Bifurcation of soliton families from linear modes in non-PT-symmetric complex potentials
• A PT-symmetric dual-core system with the sine-Gordon nonlinearity and derivative coupling
• Symmetry breaking bifurcations and excitations of solitons in linearly coupled NLS equations with PT-symmetric potentials
• Optical solitons in periodically managed PT-symmetric media
• PT-symmetric transport in non-PT-symmetric bi-layer optical arrays
• Treating Ostrogradski instability for Gallilean invariant Chern Simon's model via \mathcal{PT} symmetry
• A systematic construction of parity-time ($\mathcal{P}\mathcal{T}$)-symmetric and non-$\mathcal{P}\mathcal{T}$-symmetric complex potentials from the solutions of various real nonlinear evolution equations
• Nonlinear Schrödinger equations with amplitude-dependent Wadati potentials
• Higher-dimensional soliton generation, stability and excitations of the PT-symmetric nonlinear Schrödinger equations
• Solitons and their ghosts in PT-symmetric systems with defocusing nonlinearities
• Soliton dynamics and stability in the ABS spinor model with a PT-symmetric periodic potential
• Stability band structure for periodic states in periodic potentials
• Solitonic dynamics and excitations of the nonlinear Schrodinger equation with third-order dispersion in non-Hermitian PT-symmetric potentials