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We study the behavior of linear nonstationary shallow water waves generated by an instantaneous localized source as they propagate over and become trapped by elongated underwater banks or ridges. To find the solutions of the corresponding equations, we use an earlier-developed asymptotic approach based on a generalization of Maslov's canonical operator, which provides a relatively simple and efficient analytic-numerical algorithm for the wave field computation. An analysis of simple examplesdoi:10.1051/mmnp/20138501 fatcat:7x3cra7nnngtvjtqto2lvfghfq