Bright and kink solitons of time-modulated cubic–quintic–septic–nonic nonlinear Schrödinger equation under space-time rotated 𝒫𝒯 -symmetric potentials

This work focuses on the propagation behaviors and stabilities of solitons of a nonlinear Schrödinger equation with temporally inhomogeneous dispersion, cubic–quintic–septic–nonic nonlinearity, and group delay under Scarff II, Rosen–Morse, Harmonic, and periodic ( x , t ) plane rotated parity-time ( 𝒫𝒯 )-symmetric potentials, which governs the soliton wave transmission in a temporally inhomogeneous quasi-1D Bose-Einstein condensate system with the above effects. The novel analytical solutions of the bright solitons on zero or cw backgrounds and kink solitons under rotated 𝒫𝒯 -symmetric potentials in this system are presented for the first time. The simulation results of these three kinds of solitons show perfect consistency with the analytical ones. The bright solitons on zero or continuous-wave backgrounds show high noise immunity. While the anti-interference capability of kink soliton is connected with the form of the dispersion. These results would be advantageous for experimentally realizing stable propagation of localized nonlinear waves in highly nonlinear mediums.