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Solitons are of the important significant in many fields of nonlinear sciencesuch as nonlinear optics, Bose-Einstein condensates, plamas physics, biology,fluid mechanics, and etc.. The stable solitons have been captured not onlytheoretically and experimentally in both linear and nonlinear Schrodinger (NLS)equations in the presence of non-Hermitian potentials since the concept of theparity-time (PT)-symmetry was introduced in 1998. In this paper, we presentnovel bright solitons of the NLS equation with third-order dispersion in somecomplex PT-symmetric potentials (e.g., physically relevant PT-symmetricScarff-II-like and harmonic-Gaussian potentials). We find stable nonlinearmodes even if the respective linear PT-symmetric phases are broken. Moreover,we also use the adiabatic changes of the control parameters to excite theinitial modes related to exact solitons to reach stable nonlinear modes. Theelastic interactions of two solitons are exhibited in the third-order NLSequation with PT-symmetric potentials. Our results predict the dynamicalphenomena of soliton equations in the presence of third-order dispersion andPT-symmetric potentials arising in nonlinear fiber optics and other physicallyrelevant fields.

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