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New solutions for the propagation of long water waves over variable depth. (English) Zbl 0819.76013
Based on the linearized long-wave equation, two new analytical solutions are obtained respectively for the propagation of long surface gravity waves around a conical island and over a paraboloidal shoal. The newly derived analytical solutions are compared with several previously obtained numerical solutions, and the accuracy of those numerical solutions is discussed.
MSC:
76B15Water waves, gravity waves; dispersion and scattering, nonlinear interaction
86A05Hydrology, hydrography, oceanography