Abstract
We numerically analyzed the supratransmission phenomenon in the discrete nonlinear Schrodinger equation with the cubic–quintic nonlinearity. It has been reported that the homoclinic nonlinear band-gap threshold matches very well with the model. In the case of the cooperation between the nonlinearities (self-focusing cubic and quintic terms), the train of discrete band-gap waves overcomes the potential barrier of the first sites before merging or rebounding. In the case of competing self-focusing cubic and defocusing quintic nonlinearities, it is found that the lattice induces the generation of the train of dark solitons carried by a traveling kink and the traveling kink for chosen driving amplitude.
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