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The Cauchy problem for the one-dimensional shallow water equations with variable bottom D(x) and localized initial data is considered. The domain under consideration is confined by a vertical wall on the right, where the Neumann conditions are set, and a movable border on the left. An asymptotics of the Carrier-Greenspan transform is used to get equations with fixed boundaries and small nonlinear terms, which allows to construct (formal) asymptotics to the initial problem. Wave profile changes and its relation to the Maslov index are of interest.