Abstract
In this paper, we introduce a PT-symmetric harmonic-hyperbolic-Gaussian (HHG) potential in the nonlinear Schrödinger (NLS) equation with quintic nonlinearity. Firstly, we present the critical thresholdless PT-phase symmetry breaking in the linear regime. Secondly, we give both exact and numerical single-/double-hump solitons of the quintic NLS equations with the PT-symmetric HHG potential, and show their stabilities by studying the spectrum stability analysis and direct wave propagations. Finally, we investigate the interactions between the single-/double-hump solitons and the exotic hyperbolic secant function, as well as the adiabatic excitations of the solitons with the operation of an adiabatic switch function. All these obtained results provide a theoretical guidance for the applications of the PT-symmetric theory into diverse areas of physics.
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