Solitons in fourth-order Schrödinger equation with parity-time-symmetric extended Rosen-Morse potentials

Abstract

Abstract We investigate the fourth-order nonlinear Schrödinger equation modulated by parity-time-symmetric extended Rosen-Morse potentials. Since the imaginary part of the potentials does not vanish asymptotically, any slight fluctuations in the field can eventually cause the nonlinear modes to become unstable. Here we obtain stable solitons by adding the constraints of coefficients, which make the imaginary part of the potentials component vanish asymptotically. Furthermore, we get other fundamental stable single-hump and double-hump solitons by numerical methods. Then we consider excitations of the soliton via adiabatical change of system parameters. The results we obtained in this work provide a way to search for stable localized modes in parity-time-symmetric extended Rosen-Morse potentials with fourth-order dispersion.