Stability of solitons in Bose–Einstein condensates with cubic–quintic–septic nonlinearity and non- 𝒫𝒯 -symmetric complex potentials

This work investigates the existence and stability of soliton families in cubic–quintic–septic Gross–Pitaevskii equation under non- 𝒫𝒯 -symmetric complex potentials. The cubic and quintic nonlinearity parameters are fixed to be respective defocusing and focusing, and the septic nonlinearity parameter is defocusing or focusing. The existence and stability domains and the variety rules of chemical potentials are influenced appreciably by the septic nonlinearity parameter. For cases below phase transition, the single- and two-peak solitons with focusing septic nonlinearities and two-peak soliton with defocusing septic nonlinearity are stable at the domain with small condensate norm. The single-peak soliton with defocusing septic nonlinearity has two stable domains with small and large condensate norm. For cases above phase transition, the single- and two-peak solitons with focusing septic nonlinearities and two-peak soliton with defocusing septic nonlinearity do not have stable domain. While the single-peak soliton with defocusing septic nonlinearity has a stable domains with large condensate norm. The mutual corroborations between the linear-stability spectra and transmission under perturbations prove the reliability of the result.