On stable solitons and interactions of the generalized Gross-Pitaevskii equation with PT-and non-PT-symmetric potentials

Abstract

We report the bright solitons of the generalized Gross-Pitaevskii (GP) equation with some types of physically relevant parity-time-(PT-) and non-PT-symmetric potentials. We find that the constant momentum coefficient can modulate the linear stability and complicated transverse power-flows (not always from the gain toward loss) of nonlinear modes. However, the varying momentum coefficient Gamma(x) can modulate both unbroken linear PT-symmetric phases and stability of nonlinear modes. Particularly, the nonlinearity can excite the unstable linear mode (i.e., broken linear PT-symmetric phase) to stable nonlinear modes. Moreover, we also find stable bright solitons in the presence of non-PT-symmetric harmonic-Gaussian potential. The interactions of two bright solitons are also illustrated in PT-symmetric potentials. Finally, we consider nonlinear modes and transverse power-flows in the three-dimensional (3D) GP equation with the generalized PT-symmetric Scarf-II potential

16 pages, 23 figures

References in corpus (11)

• Making Sense of Non-Hermitian Hamiltonians
• Solitons in PT-symmetric nonlinear lattices
• Model of a PT symmetric Bose-Einstein condensate in a delta-functions double well
• Stable dark solitons in PT-symmetric dual-core waveguides
• Sagnac Interferometry Using Bright Matter-Wave Solitons
• Symmetry breaking of solitons in one-dimensional parity-time-symmetric optical potentials
• Nonlocal gap solitons in PT-symmetric periodic potentials with defocusing nonlinearity
• Bose-Einstein condensates with localized spin-orbit coupling: soliton complexes and spinor dynamics
• Coupling approach for the realization of a $\mathcal{P}\mathcal{T}$-symmetric potential for a Bose-Einstein condensate in a double well
• One-dimensional description of a Bose-Einstein condensate in a rotating closed-loop waveguide
• Cusp bifurcation in the eigenvalue spectrum of PT-symmetric Bose-Einstein condensates

Cited by in corpus (5)

• Solving forward and inverse problems of the logarithmic nonlinear Schrodinger equation with PT-symmetric harmonic potential via deep learning
• Solitons and their stability in the nonlocal nonlinear Schroedinger equation with PT-symmetric potentials
• Stable parity-time-symmetric nonlinear modes and excitations in a derivative nonlinear Schrodinger equation
• Attraction centers and PT-symmetric delta-functional dipoles in critical and supercritical self-focusing media
• Impact of near-PT symmetry on exciting solitons and interactions based on a complex Ginzburg-Landau model