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Islam, Mohammad Kamrul (2010) Near-shore behaviour of the mild-slope equation. Masters thesis, London Metropolitan University.
This research focuses on the behavior of waves in very shallow water and, in particular, we use the classical dispersion relation for wave transformation over variable bottom topography. The work supports those by others on the Mild-Slope equation but separately seeks to validate a new version of the classical Burnside dispersion relation which has recently been developed. This has been done by examining in detail a known analytical solution for waves over a curved bed profile. It is in the connection with Roseau's problem of waves on a curved bed profile and we have developed a new solution of Roseau's problem. We will find numerical solutions and asymptotic results over the Roseau's problem. Roseau used the Fourier transformation to get his solution, it is very difficult to understand. But we use Mellin transformation get a solution, it is very easy to get a solution and improve understanding. Roseau got only one solution, but our work has been to look for another exact solution
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