Stability of one and two-dimensional spatial solitons in a cubic–quintic–septimal nonlinear Schrödinger equation with fourth-order diffraction and PT-symmetric potentials

Abstract In this paper, the existence and stability of solitons in parity-time ( PT )-symmetric optical media characterized by a generic complex hyperbolic refractive index distribution with fourth-order diffraction (FOD) coefficient and higher-order nonlinearities have been investigated. For the linear case, we have demonstrated numerically that, the FOD parameter can alter the PT -breaking points. Exact analytical expressions of the localized modes are obtained respectively, in one and two dimensional nonlinear Schrodinger (NLS) equation with both self-focusing and self-defocusing Kerr, and higher-order nonlinearities for nonlinear case. The effects of both FOD and higher-order nonlinearities on the stability/instability structure of these localized modes have also been discussed with the help of linear stability analysis followed by the direct numerical simulation of the governing equation. Some stable and unstable solutions have been given and, it has been seen how higher-order self-focusing and self-defocusing nonlinearities can influence the stability/instability of the system.