Stabilization of self-steepening optical solitons in a periodic PT-symmetric potential

We numerically investigate the existence and stability dynamics of self-steepening optical solitons in a periodic PT-symmetric potential. We show that self-steepening solitons of the modified nonlinear Schr\"odinger (MNLS) equation undergo a position shift and amplitude increase during their evolution in the MNLS equation. The stabilization of solitons by an external potential is a challenging issue. This study demonstrates that the suppression of both the amplitude increase and the position shift of self-steepening solitons can be achieved by adding a periodic PT-symmetric potential to the MNLS equation.