Stable solitons and peakons, quantum information entropies, interactions, and excitations for generalized [formula omitted]-symmetric NLS equations

Abstract

In this paper, a class of physically interesting PT-symmetric δ(x)-absolute-harmonic-Gaussian (PT-δ-AHG) potentials is explored in both linear and nonlinear wave regimes. In the linear regime, we find that the PT-δ-AHG potential can make the non-Hermitian Hamiltonian possess fully-real spectra for some parameter regions. In the nonlinear regime, we find the stable solitons, and single- and double-hump peakons for both focusing and defocusing generalized nonlinear Schrödinger (NLS) equations with PT-δ-AHG potentials. Moreover, the quantum information entropies of these nonlinear modes are investigated to explore the dynamic behaviors of PT nonlinear systems. Also, the dynamic interactions of exact solitons with incident solitary waves are discussed. Finally, we find that these bright solitons, single- and double-hump peakons can still stably propagate by means of adiabatic excitations, i.e., by slowly changing the parameters of the PT-δ-AHG potential, which implies that one can stably modulate the PT optical solitons. These interesting results will be helpful to further explore the relative PT nonlinear wave phenomena, and to design some physical experiments.