Solitonic dynamics and excitations of the nonlinear Schrödinger equation with third-order dispersion in non-Hermitian PT-symmetric potentials

Solitons are of the important significant in many fields of nonlinear science such as nonlinear optics, Bose-Einstein condensates, plamas physics, biology, fluid mechanics and etc. The stable solitons have been captured not only theoretically and experimentally in both linear and nonlinear Schrödinger (NLS) equations in the presence of non-Hermitian potentials since the concept of the parity-time [inline-graphic not available: see fulltext]-symmetry was introduced in 1998. In this paper, we present novel bright solitons of the NLS equation with third-order dispersion in some complex [inline-graphic not available: see fulltext]-symmetric potentials (e.g., physically relevant [inline-graphic not available: see fulltext]-symmetric Scarff-II-like and harmonic-Gaussian potentials). We find stable nonlinear modes even if the respective linear [inline-graphic not available: see fulltext]-symmetric phases are broken. Moreover, we also use the adiabatic changes of the control parameters to excite the initial modes related to exact solitons to reach stable nonlinear modes. The elastic interactions of two solitons are exhibited in the third-order NLS equation with [inline-graphic not available: see fulltext]-symmetric potentials. Our results predict the dynamical phenomena of soliton equations in the presence of third-order dispersion and [inline-graphic not available: see fulltext]-symmetric potentials arising in nonlinear fiber optics and other physically relevant fields.