The Evolution of Longwave Solutions to the Nonlinear Schrödinger Equation

dc.contributorVirginia Techen
dc.contributor.authorCramer, Mark S.en
dc.contributor.authorWatson, Layne T.en
dc.contributor.departmentBiomedical Engineering and Mechanicsen
dc.contributor.departmentComputer Scienceen
dc.date.accessed2014-04-04en
dc.date.accessioned2014-04-24T18:34:20Zen
dc.date.available2014-04-24T18:34:20Zen
dc.date.issued1984en
dc.description.abstractIn water of moderate depth, the behavior of small perturbations superimposed on Stokes wave trains is described by the nonlinear (cubic) Schrödinger equation. In the present study wave‐like solutions to this equation are examined, and it is shown that when these perturbations are neutrally stable and sufficiently long, solutions to the Schrödinger equation may be approximated by the well‐known Korteweg–deVries equation. As a result, sufficiently long perturbations to Stokes wave trains may be regarded as mathematically analogous to those imposed on a free surface separating two fluids of different densities. This result is established independently by singular perturbation techniques, numerical computation, and comparison of exact stationary wave solutions.en
dc.identifier.citationCramer, M. S.; Watson, L. T., "The evolution of longwave solutions to the nonlinear Schrödinger equation," Phys. Fluids 27, 821 (1984); http://dx.doi.org/10.1063/1.864710en
dc.identifier.doihttps://doi.org/10.1063/1.864710en
dc.identifier.issn1070-6631en
dc.identifier.urihttp://hdl.handle.net/10919/47666en
dc.identifier.urlhttp://scitation.aip.org/content/aip/journal/pof1/27/4/10.1063/1.864710en
dc.language.isoen_USen
dc.publisherAIP Publishingen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.titleThe Evolution of Longwave Solutions to the Nonlinear Schrödinger Equationen
dc.title.serialPhysics of Fluidsen
dc.typeArticle - Refereeden
dc.type.dcmitypeTexten
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