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초록

In this study, we develop analytical solutions for long waves propagating over several types of axis-symmetric topographies where the water depth varies in an arbitrary power of radial distance. The first type is a cylindrical island mounted on a shoal. The second type is a circular island. To get the solution, the methods of separation of variables, Taylor series expansion and Frobenius series are used. Developed analytical solutions are validated by comparing with previously developed analytical solutions. We also investigate various cases with different incident wave periods, radii of the shoal, and the powers of radial distance.

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