| Summary: | We study on the nonlinear tunneling effect of snakelike self-similar waves of the nonlinear Schrödinger equation with gains in an asymmetric dual-core waveguide amplifier with a long-period grating. Using the self-similar transformation we find the bright and dark snakelike self-similar waves with W-, U-, and bell-shaped profiles. As an application, we investigate the nonlinear tunneling effect of these optical structures under some constraint conditions. The results show that the snakelike self-similar waves can similarly pass through the nonlinear barrier or well and can be effectively controlled by adjusting the source amplitude and the long-period grating. Our results may have potential applications for improving channel capacity in the graded-index dual-core waveguide amplifiers with a long-period grating. Keywords: Nonlinear tunneling effect, Snakelike self-similar waves, Asymmetric dual-core waveguide amplifier
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