J Austral Math Soc Ser B 35 pp382--395, 1994.

Solution of the problem of scattering of water waves by a nearly vertical plate

L. Vijaya Bharathi, A. Chakrabarti, B. N. Mandal and S. Banerjee

Abstract

An approximate solution is determined for the problem of scattering of water waves by a nearly vertical plate, by reducing it to two mixed boundary-value problems (BVP) for Laplace's equation, using perturbation techniques. While the solution of one of these BVP is well-known, the other BVPs is reduced to the problem of solving two uncoupled Riemann-Hilbert problems, and the complete solution of the problem under consideration up to first-order accuracy is derived with a special assumption on the shape of the plate and a related approximation. Known results involving the reflection and transmission coefficients are reproduced.

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Authors

L. Vijaya Bharathi

A. Chakrabarti

Department of Mathematics, Indian Institute of Science, Bangalore-12, India.

B. N. Mandal

Physical and Earth Sciences Division, Indian Statistical Institute, Calcutta-35, India.

S. Banerjee

Calcutta Mathematical Society, Calcutta-9, India.