Abstract
The similarity transformation between the inhomogeneous (n+1)-dimensional generalized nonlinear Schrödinger equation (NLSE) and the constant-coefficient NLSE in optical fibers is constructed with some constraints for the parameters of the medium. The exact balance between the dispersion/diffraction, nonlinearity and the gain/loss produces self-similar waves (similaritons). As an example, we investigate the nonlinear tunneling effect of flat-top similariton. The results show that the effects of dispersion barrier and well for the similariton are similar to that of nonlinear well and barrier, respectively.
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