We construct the relation between the variable coefficient nonlinear Schr?dinger equations with power-law nonlinearity and the constant coefficient one via a transformation. Based on this transformation, we analytically obtain the closed-form bright and dark soliton solutions for variable coefficient nonlinear Schr?dinger equations with power-law nonlinearity, third-order dispersion and self-steepening effect. The dynamic behaviors of bright and dark solitons in dispersion-decreasing fibers with hyperbolic, exponential, linear, logarithmic and Gaussian profiles are analyzed.
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