Avoidance of instability of a superluminal Gaussian light pulse via control of nonlinear coherence Kerr effect in a gain-assisted medium

We investigate nonlinear Kerr-induced coherence effect on a superluminal probing light pulse in a gain-assisted N-type 4-level atomic system via an intense monochromatic laser field. The dispersion exhibits a novel, interesting and useful two-paired double gain lines processes. The system displays lossless characteristics similar to [L. J. Wang, A. Kuzmich, A. Dogariu, Nature $\mathbf{\text{406}}$, 277 (2000)] but with advantages of \emph{multiple} $\mathbf{\text{controllable}}$ anomalous regions, \emph{significantly enhanced} superluminal behavior and $\mathbf{\text{relaxed}}$ temperature, states of matter regardless of its isotropic or anisotropic conditions. Unlike the instability in [A. M. Akulshin, S. Barreiro, and A. Lezama, Phys. Rev. Lett. $\mathbf{\text{82}}$, 4277 (1999)], the present system also \emph{overcomes the instable-limit} by the Kerr-induced coherence effect in the system. Indeed, the coherence enhances the group velocity remarkably by at least $-30ms$ more than of an instable Kerr-free system with almost negligible distortion in the retrieved pulse.