title: Transversally periodic solitary gravity-capillary waves.
abstract: When both gravity and surface tension effects are present, surface solitary water waves are known to exist in both two- and three-dimensional infinitely deep fluids. We describe here solutions bridging these two cases: travelling waves which are localized in the propagation direction and periodic in the transverse direction. These transversally periodic gravity-capillary solitary waves are found to be of either elevation or depression type, tend to plane waves below a critical transverse period and tend to solitary lumps as the transverse period tends to infinity. The waves are found numerically in a Hamiltonian system for water waves simplified by a cubic truncation of the Dirichlet-to-Neumann operator. This approximation has been proved to be very accurate for both two- and three-dimensional computations of fully localized gravity-capillary solitary waves. The stability properties of these waves are then investigated via the time evolution of perturbed wave profiles.
authors.affiliation: Department of Mathematical Sciences , University of Bath , Bath BA2 7AY, UK.
authors.forename: Paul A
authors.initials: PA
authors.lastname: Milewski
authors.affiliation: Department of Mathematics , University College London , Gower Street, London WC1E 6BT, UK.
authors.forename: Zhan
authors.initials: Z
authors.lastname: Wang
keywords: breather; gravity–capillary; periodic wave; solitary wave