Stable 2D localized modes in anisotropic media with harmonic and \(\mathcal{PT}\)-symmetric potentials
This paper is concerned with analytical spatial localized mode solutions of a two-dimensional nonlinear Schrödinger equation and the corresponding linear stability of these solutions. The nonlinear Schrödinger equation discussed has constant diffraction and nonlinearity in \(\mathcal{PT}\)-symmetric potential. The results show that spatial solitons in a 2D complex \(\mathcal{PT}\)-symmetric Rosen-Morse potential are unstable, and spatial solitons in the \(\mathcal{PT}\)-symmetric potentials with \(m=1,2,3\) are stable in the self-focusing medium while unstable in the self-defocusing medium. Also, the analytical spatial localized mode solutions in anisotropic media with harmonic and \(\mathcal{PT}\)-symmetric potentials are derived based on the relation between two nonlinear Schrödinger equations with variable and constant diffraction and nonlinearity. At last, the diffraction management of spatial localized modes in \(\mathcal{PT}\)-symmetric complex potentials is investigated, and direct numerical simulations are performed to demonstrate their results.
scientific article; zbMATH DE number 6535642