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In this paper, the phenomenon of band gaps and Anderson localization of waterwaves over one-dimensional periodic and random bottoms is investigated by thetransfer matrix method. The results indicate that the range of localization inrandom bottoms can be coincident with the band gaps for the correspondingperiodic bottoms. Inside the gap or localization regime, a collective behaviorof water waves appears. The results are also compared with acoustic and opticalsituations.Comment: 3 pages, five figure

Band gaps and localization of water waves over one-dimensional topographical bottoms