Nonlinear modes in the harmonic PT-symmetric potential

Abstract

We study the families of nonlinear modes described by the nonlinear Schrödinger equation with the PT-symmetric harmonic potential $x^2-2i\alpha x$. The found nonlinear modes display a number of interesting features. In particular, we have observed that the modes, bifurcating from the different eigenstates of the underlying linear problem, can actually belong to the same family of nonlinear modes. We also show that by proper adjustment of the coefficient $\alpha$ it is possible to enhance stability of small-amplitude and strongly nonlinear modes comparing to the well-studied case of the real harmonic potential.

7 pages, 2 figures; accepted to Phys. Rev. A

References in corpus (8)

• Physical realization of $\mathcal{P}\mathcal{T}$-symmetric potential scattering in a planar slab waveguide
• Conservation relations and anisotropic transmission resonances in one-dimensional PT-symmetric photonic heterostructures
• Solitons in PT-symmetric nonlinear lattices
• Nonlocal bright spatial solitons in defocusing Kerr media supported by PT symmetric potentials
• Stability of localized modes in PT-symmetric nonlinear potentials
• Nonlinear modes for the Gross-Pitaevskii equation -- demonstrative computation approach
• Interactions of Hermitian and non-Hermitian Hamiltonians
• Stability of excited states of a Bose-Einstein condensate in an anharmonic trap

Cited by in corpus (49)

• Nonlinear waves in $\mathcal{P}\mathcal{T}$-symmetric systems
• Nonlinear switching and solitons in PT-symmetric photonic systems
• Dark solitons and vortices in PT-symmetric nonlinear media: from spontaneous symmetry breaking to nonlinear PT phase transitions
• Breathers in PT-symmetric optical couplers
• Stable dark solitons in PT-symmetric dual-core waveguides
• 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
• Solitons in a nonlinear Schrodinger equation with PT-symmetric potentials and inhomogeneous nonlinearity: stability and excitation of nonlinear modes
• 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
• All-real spectra in optical systems with arbitrary gain and loss distributions
• Families of stationary modes in complex potentials
• Symmetry breaking of solitons in two-dimensional complex potentials
• Necessity of PT symmetry for soliton families in one-dimensional complex potentials
• Solitons in $\mathcal{P}\mathcal{T}$-symmetric periodic systems with the quadratic nonlinearity
• On stable solitons and interactions of the generalized Gross-Pitaevskii equation with PT-and non-PT-symmetric potentials
• Jamming anomaly in $\mathcal{P}\mathcal{T}$-symmetric systems
• Revisiting the PT-symmetric Trimer: Bifurcations, Ghost States and Associated Dynamics
• Nonlinear localized modes in PT-symmetric optical media with competing gain and loss
• Stable parity-time-symmetric nonlinear modes and excitations in a derivative nonlinear Schrodinger equation
• Stability of soliton families in nonlinear Schroedinger equations with non-parity-time-symmetric complex potentials
• 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
• Tunable nonlinear PT-symmetric defect modes with an atomic cell
• Analytical stable Gaussian soliton supported by a parity-time-symmetric potential with power-law nonlinearity
• Nonlinear Topological Edge States in a non-Hermitian Array of Optical Waveguides Embedded in an Atomic Gas
• Stationary modes and integrals of motion in nonlinear lattices with PT-symmetric linear part
• Impact of near-PT symmetry on exciting solitons and interactions based on a complex Ginzburg-Landau model
• PT-symmetric lattices with spatially extended gain/loss are generically unstable
• Nonlinear light behaviors near phase transition in non-parity-time-symmetric complex waveguides
• PT-symmetric quantum oscillator in an optical cavity
• Quasi-one-dimensional harmonically trapped quantum droplets
• Eigenvalue Bifurcation in Doubly Nonlinear Problems with an Application to Surface Plasmon Polaritons
• Effects of the third-order dispersion on continuous waves in complex potentials
• Formations and dynamics of two-dimensional spinning asymmetric quantum droplets controlled by a PT-symmetric potential
• Small-amplitude nonlinear modes under the combined effect of the parabolic potential, nonlocality and $\mathcal{P}\mathcal{T}$ symmetry
• Krein signature for instability of $\mathcal{P}\mathcal{T}$-symmetric states
• 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
• Global search for localised modes in scalar and vector nonlinear Schrödinger-type equations
• On the Thomas-Fermi approximation of the ground state in a PT-symmetric confining potential
• Higher-dimensional soliton generation, stability and excitations of the PT-symmetric nonlinear Schrödinger equations
• Spectral and Dynamical Properties of the Fractional Nonlinear Schrödinger Equation under Harmonic Confinement
• Solitons and their ghosts in PT-symmetric systems with defocusing nonlinearities
• Eigenvalues bifurcating from the continuum in two-dimensional potentials generating non-Hermitian gauge fields
• Stability band structure for periodic states in periodic potentials
• Exponential asymptotics for solitons in PT-symmetric periodic potentials
• On non-existence of continuous families of stationary nonlinear modes for a class of complex potentials
• Solitonic dynamics and excitations of the nonlinear Schrodinger equation with third-order dispersion in non-Hermitian PT-symmetric potentials