Necessity of PT symmetry for soliton families in one-dimensional complex potentials

Abstract

For the one-dimensional nonlinear Schroedinger equation with a complex potential, it is shown that if this potential is not parity-time (PT) symmetric, then no continuous families of solitons can bifurcate out from linear guided modes, even if the linear spectrum of this potential is all real. Both localized and periodic non-PT-symmetric potentials are considered, and the analytical conclusion is corroborated by explicit examples. Based on this result, it is argued that PT-symmetry of a one-dimensional complex potential is a necessary condition for the existence of soliton families.

14 pages, 3 figures

References in corpus (9)

• Solitons in PT-symmetric nonlinear lattices
• Bifurcations and stability of gap solitons in periodic potentials
• Supersymmetry-generated complex optical potentials with real spectra
• $\mathcal{P}\mathcal{T}$-symmetry breaking in a necklace of coupled optical waveguides
• Vector solitons in PT-symmetric lattices
• Discrete solitons in PT-symmetric lattices
• Localized modes in ${\chi }^{(2)}$ media with $\PT$-symmetric localized potential
• Stationary modes and integrals of motion in nonlinear lattices with PT-symmetric linear part
• Can parity-time-symmetric potentials support continuous families of non-parity-time-symmetric solitons?

Cited by in corpus (21)

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• Nonlinear switching and solitons in PT-symmetric photonic systems
• 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
• Stable localized modes in asymmetric waveguides with gain and loss
• Families of stationary modes in complex potentials
• Stability of soliton families in nonlinear Schroedinger equations with non-parity-time-symmetric complex potentials
• Attraction centers and PT-symmetric delta-functional dipoles in critical and supercritical self-focusing media
• One-parameter families of supersymmetric isospectral potentials from Riccati solutions in function composition form
• Spinor solitons and their $\mathcal{P}\mathcal{T}$-symmetric offspring
• Designing lasing and perfectly absorbing potentials
• PT-symmetric sine-Gordon breathers
• Dynamical control of solitons in a parity-time-symmetric coupler by periodic management
• Shifted one-parameter supersymmetric family of quartic asymmetric double-well potentials
• New families of non-parity-time-symmetric complex potentials with all-real spectra
• Robust PT symmetry of two-dimensional fundamental and vortex solitons supported by spatially modulated nonlinearity
• Making the PT symmetry unbreakable
• PT-symmetric and antisymmetric nonlinear states in a split potential box
• "Striped" Rectangular Rigid Box with Hermitian and non-Hermitian $\mathcal{P}\mathcal{T}$ Symmetric Potentials
• Analytical construction of soliton families in one- and two-dimensional nonlinear Schrödinger equations with non-parity-time-symmetric complex potentials
• Construction of non-PT-symmetric complex potentials with all-real spectra