 Stable three-dimensional waves of nearly permanent form on deep waterWalter Craig, Diane M. Henderson, Maribeth Oscamou and Harvey Segur Mathematics and Computers in Simulation (MATCOM), 2007, vol. 74, issue 2, 135-144 Abstract: Consider a uniform train of surface waves with a two-dimensional, bi-periodic surface pattern, propagating on deep water. One approximate model of the evolution of these waves is a pair of coupled nonlinear Schrödinger equations, which neglects any dissipation of the waves. We show that in this model, such a wave train is linearly unstable to small perturbations in the initial data, because of a Benjamin–Feir-type instability. We also show that when the model of coupled equations is generalized to include appropriate wave damping, the corresponding wave train is linearly stable to perturbations in the initial data. Therefore, according to the damped model, the two-dimensional surface wave patterns studied by Hammack et al. [J.L. Hammack, D.M. Henderson, H. Segur, Progressive waves with persistent, two-dimensional surface patterns in deep water, J. Fluid Mech. 532 (2005) 1–51] are linearly stable in the presence of wave damping. Keywords: Stability water waves, Two-dimensional patterns, Nonlinear Schrödinger equations, Dissipation, Benjamin–Feir instability, Modulational instability (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:74:y:2007:i:2:p:135-144 DOI: 10.1016/j.matcom.2006.10.032 Access Statistics for this article Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier |
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