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Single-hump and double-hump solitons in a symmetric complex potential

In this paper, we have studied the single-hump and double-hump solitons having parity - time () symmetric complex potential in a medium with cubic nonlinearity. The system has been analyzed for the stationary states and the dynamical states in the linear and nonlinear regime. The system undergoes spontaneous symmetric phase transition from the symmetric region to the broken symmetric region depending on the strength of the imaginary part of the potential. The coefficient of the imaginary part of the potential at which the phase transition occurs is known as the threshold value. The symmetric phase transition point has been studied by varying the strength of real part of the potential and the coefficient of the nonlinearity. The stable solitons are formed for low values of the coefficients of imaginary part of the potential and nonlinearity. We have analyzed the stability of the solitons using Bogoliubov–De–Genes equations.