Transversally periodic solitary gravity-capillary waves

Paul A. Milewski, Zhan Wang

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

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.

Original languageEnglish (US)
Article number20130537
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume470
Issue number2161
DOIs
StatePublished - Jan 8 2013

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • General Engineering
  • General Physics and Astronomy

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