Nonlinear localized modes in PT-symmetric Rosen-Morse potential well

Abstract

We report the existence and properties of localized modes described by nonlinear Schroedinger equation with complex PT-symmetric Rosen-Morse potential well. Exact analytical expressions of the localized modes are found in both one dimensional and two-dimensional geometry with self-focusing and self-defocusing Kerr nonlinearity. Linear stability analysis reveals that these localized modes are unstable for all real values of the potential parameters although corresponding linear Schroedinger eigenvalue problem possesses unbroken PT-symmetry. This result has been verified by the direct numerical simulation of the governing equation. The transverse power flow density associated with these localized modes has also been examined.

Accepted for publication in Physical Review A

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Cited by in corpus (24)

• Nonlinear waves in $\mathcal{P}\mathcal{T}$-symmetric systems
• Integrable $\mathcal{P}T$-symmetric local and nonlocal vector nonlinear Schrödinger equations: a unified two-parameter model
• Rational Solitons in the Parity-Time-Symmetric Nonlocal Nonlinear Schrödinger Model
• 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
• Nonlinear localized modes in PT-symmetric optical media with competing gain and loss
• Optical solitons in media with focusing and defocusing saturable nonlinearity and a parity-time-symmetric external potential
• Data driven soliton solution of the nonlinear Schrödinger equation with certain $\mathcal{P}\mathcal{T}$-symmetric potentials via deep learning
• Analytical stable Gaussian soliton supported by a parity-time-symmetric potential with power-law nonlinearity
• Impact of near-PT symmetry on exciting solitons and interactions based on a complex Ginzburg-Landau model
• Exactly solvable Wadati potentials in the PT-symmetric Gross-Pitaevskii equation
• Dissipative optical solitons in asymmetric Rosen-Morse potential
• Generalized Dimers and their Stokes-variable Dynamics
• Constructing Solvable Models of Vector Non-linear Schrodinger Equation with Balanced Loss and Gain via Non-unitary transformation
• Effects of the third-order dispersion on continuous waves in complex potentials
• Integral Transforms and $\mathcal{P}\mathcal{T}$-symmetric Hamiltonians
• Supersymmetry of $\mathcal{P}\mathcal{T}$- symmetric tridiagonal Hamiltonians
• Unidirectional segregation of Bright-Bright soliton through a $\mathcal{P}\mathcal{T}$-symmetric potential
• Scattering in a varying mass PT symmetric double heterojunction
• Non-linear Schr$\ddot{o}$dinger equation with time-dependent balanced loss-gain and space-time modulated non-linear interaction
• 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
• Classical Hamiltonian Systems with Balanced loss and gain
• Higher-dimensional soliton generation, stability and excitations of the PT-symmetric nonlinear Schrödinger equations
• Stability band structure for periodic states in periodic potentials