Stabilization of solitons in PT models with supersymmetry by periodic management

Abstract

We introduce a system based on dual-core nonlinear waveguides with the balanced gain and loss acting separately in the cores. The system features a "supersymmetry" when the gain and loss are equal to the inter-core coupling. This system admits a variety of exact solutions (we focus on solitons), which are subject to a specific subexponential instability. We demonstrate that the application of a "management", in the form of periodic simultaneous switch of the sign of the gain, loss, and inter-coupling, effectively stabilizes solitons, without destroying the supersymmetry. The management turns the solitons into attractors, for which an attraction basin is identified. The initial amplitude asymmetry and phase mismatch between the components transforms the solitons into quasi-stable breathers.

In press EPL 2011

References in corpus (5)

• Making Sense of Non-Hermitian Hamiltonians
• Visualization of Branch Points in PT-Symmetric Waveguides
• Unidirectional Nonlinear PT-symmetric Optical Structures
• Physical realization of $\mathcal{P}\mathcal{T}$-symmetric potential scattering in a planar slab waveguide
• Solitons in PT-symmetric nonlinear lattices

Cited by in corpus (42)

• Nonlinear waves in $\mathcal{P}\mathcal{T}$-symmetric systems
• Nonlinear switching and solitons in PT-symmetric photonic systems
• Breathers in PT-symmetric optical couplers
• Stable dark solitons in PT-symmetric dual-core waveguides
• $\mathcal{P}\mathcal{T}$-symmetry breaking in a necklace of coupled optical waveguides
• Vector solitons in PT-symmetric lattices
• A solvable model for solitons pinned to a PT-symmetric dipole
• Linear and Nonlinear PT-symmetric Oligomers: A Dynamical Systems Analysis
• Solitons in $\mathcal{P}\mathcal{T}$-symmetric periodic systems with the quadratic nonlinearity
• Revisiting the PT-symmetric Trimer: Bifurcations, Ghost States and Associated Dynamics
• Tailoring $\mathcal{P}\mathcal{T}$-symmetric soliton switch
• Bragg gap solitons in $\mathcal{P}\mathcal{T}$ symmetric lattices with competing nonlinearity
• Symmetry breaking in dipolar matter-wave solitons in dual-core couplers
• Parity-time symmetric optical coupler with birefringent arms
• Solitons in PT-symmetric ladders of optical waveguides
• PT-symmetric coupler with a coupling defect: soliton interaction with exceptional point
• Supersymmetry-guided method for mode selection and optimization in coupled systems
• Analytical stable Gaussian soliton supported by a parity-time-symmetric potential with power-law nonlinearity
• $\mathcal{P}\mathcal{T}$-symmetric coupler with ${\chi }^{(2)}$ nonlinearity
• Dynamics of higher-order solitons in regular and PT-symmetric nonlinear couplers
• PT-symmetric lattices with spatially extended gain/loss are generically unstable
• Analytical results for a parity-time symmetric two-level system under synchronous combined modulations
• CP symmetry in optical systems
• PT-symmetry, indefinite damping and dissipation-induced instabilities
• Multisoliton Newton's cradles and supersolitons in regular and PT-symmetric nonlinear couplers
• Exact control of parity-time symmetry in periodically modulated nonlinear optical couplers
• PT-symmetry Management in Oligomer Systems
• Quasi-energies, parametric resonances, and stability limits in ac-driven $\mathcal{P}\mathcal{T}$-symmetric systems
• Generalized Dimers and their Stokes-variable Dynamics
• PT-symmetric sine-Gordon breathers
• Solitons in $\mathcal{P}\mathcal{T}$-symmetric systems with spin-orbit coupling and critical nonlinearity
• Dynamical control of solitons in a parity-time-symmetric coupler by periodic management
• Switching dynamics of femtosecond solitons in parity-time-symmetric coupled optical waveguides
• Integrable Local and Non-local Vector Non-linear Schrodinger Equation with Balanced loss and Gain
• Constructing Solvable Models of Vector Non-linear Schrodinger Equation with Balanced Loss and Gain via Non-unitary transformation
• Tunable nonlinear spectra of anti-directional couplers
• Solvable Limits of a class of generalized Vector Nonlocal Nonlinear Schrödinger equation with balanced loss-gain
• A PT-symmetric dual-core system with the sine-Gordon nonlinearity and derivative coupling
• Optical solitons in periodically managed PT-symmetric media
• Non-linear Schr$\ddot{o}$dinger equation with time-dependent balanced loss-gain and space-time modulated non-linear interaction
• Solitons and their ghosts in PT-symmetric systems with defocusing nonlinearities
• Classical Hamiltonian Systems with Balanced loss and gain