Nonlinear tunneling of nonautonomous optical solitons in combined nonlinear Schrödinger and Maxwell-Bloch systems

We consider the nonlinear Schrödinger-Maxwell-Bloch (NLS-MB) equation with variable coefficients. We construct the Lax pair for the NLS-MB system through AKNS formalism. We derived the two-soliton solution using the Darboux transformation. Finally we demonstrate the nonlinear tunneling of two solitons through dispersion and the nonlinear barrier or well. Our result shows that solitons can be compressed through the tunneling barrier or well with exponential decay for the special choice of variable coefficients.