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Linear stability spectra of self-steepening solitons of Eq. (2) (with $s=0.1$, $\beta=1$, $\mu=1$) in Eq. (2). (a) $V_0=0, W_0=0$; (b) $V_0=0.7, W_0=0$; (c) $V_0=0.7, W_0=0.3$; (d) $V_0=0.7, W_0=-0.3$.
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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 soli...
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