Robust PT symmetry of two-dimensional fundamental and vortex solitons supported by spatially modulated nonlinearity

Abstract

The real spectrum of bound states produced by PT-symmetric Hamiltonians usually suffers breakup at a critical value of the strength of gain-loss terms, i.e., imaginary part of the complex potential. On the other hand, it is known that the PT-symmetry can be made unbreakable in a one-dimensional (1D) model with self-defocusing nonlinearity whose strength grows fast enough from the center to periphery. The model is nonlinearizable, i.e., it does not have a linear spectrum, while the (unbreakable) PT symmetry in it is defined by spectra of continuous families of nonlinear self-trapped states (solitons). Here we report results for a 2D nonlinearizable model whose PT symmetry remains unbroken for arbitrarily large values of the gain-loss coeffcient. Further, we introduce an extended 2D model with the imaginary part of potential ~ xy in the Cartesian coordinates. The latter model is not a PT-symmetric one, but it also supports continuous families of self-trapped states, thus suggesting an extension of the concept of the PT symmetry. For both models, universal analytical forms are found for nonlinearizable tails of the 2D modes, and full exact solutions are produced for particular solitons, including ones with the unbreakable PT symmetry, while generic soliton families are found in a numerical form. The PT-symmetric system gives rise to generic families of stable single- and double-peak 2D solitons (including higher-order radial states of the single-peak solitons), as well as families of stable vortex solitons with winding numbers m = 1, 2, and 3. In the model with imaginary potential ~ xy, families of single-and multi-peak solitons and vortices are stable if the imaginary potential is subject to spatial confinement. In an elliptically deformed version of the latter model, an exact solution is found for vortex solitons with m = 1.

to be published in Scientific Reports. arXiv admin note: text overlap with arXiv:1802.08783

References in corpus (11)

• 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
• Exponentially Fragile PT-Symmetry in Lattices with Localized Eigenmodes
• Bragg solitons in nonlinear PT-symmetric periodic potentials
• Unbreakable PT-symmetry of solitons supported by inhomogeneous defocusing nonlinearity
• Symmetry breaking of solitons in two-dimensional complex potentials
• Hamiltonian formulation of the standard $\mathcal{P}\mathcal{T}$-symmetric nonlinear Schrödinger dimer
• Soliton dynamics in symmetric and non-symmetric complex potentials
• Metric Operators for Quasi-Hermitian Hamiltonians and Symmetries of Equivalent Hermitian Hamiltonians
• Stabilization of the coupled pendula chain under parametric PT-symmetric driving force

Cited by in corpus (2)

• Attraction centers and PT-symmetric delta-functional dipoles in critical and supercritical self-focusing media
• Nonlinear nonuniform $\mathcal{P}\mathcal{T}$-symmetric Bragg grating structures