%0 Journal Article
%A Motygin, Oleg V
%A McIver, Philip
%T On uniqueness in the problem of gravity–capillary water waves above submerged bodies
%D 2009
%R 10.1098/rspa.2009.0012
%J Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science
%X In this paper, we consider the two-dimensional linear problem of wave–body interaction with surface tension effects being taken into account. We suggest a criterion for unique solvability of the problem based on symmetrization of boundary integral equations. The criterion allows us to develop an algorithm for detecting non-uniqueness (finding trapped modes) for given geometries of bodies; examples of numerical computation of trapped modes are given. We also prove a uniqueness theorem that provides simple bounds for the possible non-uniqueness parameters.
%U http://rspa.royalsocietypublishing.org/content/royprsa/early/2009/03/06/rspa.2009.0012.full.pdf