W-shaped solitons under inhomogeneous self- defocusing kerr nonlinearity

We demonstrate W-shaped solitons sustained under the inhomogeneous self-defocusing Kerr nonlinearity in the nonlinear Schrodinger equation. These solitons are dark or gray beams that ride on a constant background. We obtain different types of W-shaped solitons when the parameters in the equation are set suitably. All W-shaped solitons found are stable, established by the linear stability analysis, and checked by direct numerical simulation. Power defect arising in these soliton families is also investigated, and we find that the power defect change with the propagation constant is nearly linear. Besides standard perturbed propagation, we also display propagation with modulated parameters and find that the sudden variation of the appropriate parameter leads to unacceptable distortions and instability in the solution, while the gradual change of the parameter restores regular stable behavior.