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Nonlinear evolution of the self-steepening soliton of Eq. (2) (with $\beta=1$, $s=0.3$, $V_0=0.7$) in Eq. (2). (a) Optical pulses at $z=0$ and $z=50$ for $W_0=-0.3$. (b) Optical pulses at $z=0$ and $z=50$ for $W_0=-0.209$. (c) Amplitudes as a function of the propagation distance $z$.
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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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