Solitons and their stability in the nonlocal nonlinear Schroedinger equation with PT-symmetric potentials

Abstract

We report localized nonlinear modes of the self-focusing and defocusing nonlocal nonlinear Schroedinger equation with the generalized PT-symmetric Scarf-II, Rosen-Morse, and periodic potentials. Parameter regions are presented for broken and unbroken PT-symmetric phases of linear bounded states and the linear stability of the obtained solitons. Moreover, we numerically explore the dynamical behaviors of solitons and find stable solitons for some given parameters.

11 pages, 5 figures

References in corpus (6)

• Making Sense of Non-Hermitian Hamiltonians
• Lie symmetries and solitons in nonlinear systems with spatially inhomogeneous nonlinearities
• Solitons in PT-symmetric nonlinear lattices
• Localized nonlinear waves in systems with time- and space-modulated nonlinearities
• Integrable $\mathcal{P}T$-symmetric local and nonlocal vector nonlinear Schrödinger equations: a unified two-parameter model
• Bifurcations and stability of gap solitons in periodic potentials

Cited by in corpus (5)

• Data driven soliton solution of the nonlinear Schrödinger equation with certain $\mathcal{P}\mathcal{T}$-symmetric potentials via deep learning
• Attraction centers and PT-symmetric delta-functional dipoles in critical and supercritical self-focusing media
• Nonlocal Nonlinear Schrodinger Equation on Metric Graphs
• Solvable Limits of a class of generalized Vector Nonlocal Nonlinear Schrödinger equation with balanced loss-gain
• Higher-dimensional soliton generation, stability and excitations of the PT-symmetric nonlinear Schrödinger equations