Abstract
The nonlinear Schrödinger equation with variable coefficient in water waves is studied, and a nonautonomous superposed Akhmediev breather solution in certain parameter conditions is derived via a one-to-one relation between this equation and the standard nonlinear Schrödinger equation. Based on this solution, the controllable behaviors for the superposed Akhmediev breather are studied in the periodic distributed amplification system and the dispersion decreasing system. The propagation behaviors of Akhmediev breather are influenced by the relation between the maximum Xm of the effective horizontal coordinate and X0 based on the peak of Akhmediev breather.
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