numerical analysis of stability for temporal bright solitons in a pt-symmetric nldc

Pt-symmetry is one of the interesting topics in quantum mechanics and optics. one of the demonstration of pt-symmetric effects in optics is appeared in the nonlinear directional coupler (nldc). in the paper we numerically investigate the stability of temporal bright solitons propagate in a pt-symmetric nldc by considering gain in bar and loss in cross. by using the analytical solutions of perturbed eigenfunctions and corresponding eigenvalues the stability of temporal bright solitons is studied numerically. three perturbed eigenfunctions corresponding to the two eigenvalues are examined for stability. the results show that the two degenerate eigenfunctions are unstable while other one is stable which have important result that the eigenfunctions are equilibrium function but not stable for all cases. stability is tested by using energy of perturbed soliton that propagate thought the length of nldc. in addition, the behavior of solitons under instable perturbation in a pt-symmetric nldc can be used to design integrated optics at nano scales, for ultrafast all optical communication systems and logic gates.