Eigenfunction expansion method for water wave scattering by small undulation

Abstract

The problem involving the scattering of surface water waves by small undulation of a sea-bed has been solved completely, by utilizing the eigenfunction expansion method leading to the mathematical problem of solving over-determined system of linear algebraic equations. Such an over-determined system of linear algebraic equations is best solved by the method of least-squares and numerical results for useful practical quantities such as the reflection and transmission coefficients are obtained