Skip to main content Accessibility help
×
Home
Hostname: page-component-568f69f84b-h2zp4 Total loading time: 0.143 Render date: 2021-09-19T18:38:51.514Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": true, "newCiteModal": false, "newCitedByModal": true, "newEcommerce": true, "newUsageEvents": true }

Estimates for the three-wave interaction of surface water waves

Published online by Cambridge University Press:  24 October 2003

GUIDO SCHNEIDER
Affiliation:
Mathematisches Institut I, Universität Karlsruhe, D-76128 Karlsruhe, Germany email: guido.schneider@mathematik.uni-karlsruhe.de
C. EUGENE WAYNE
Affiliation:
Department of Mathematics and Center for BioDynamics, Boston University, Cummington St., Boston, MA 02215, USA email: cew@math.bu.edu

Abstract

The equations for three-wave interaction describe the resonant, quadratic, nonlinear interaction of three waves. They are obtained as amplitude equations in an asymptotic reduction of the basic equations of nonlinear optics, fluid mechanics, and plasma physics. These equations are completely integrable and have been the subject of intensive research in the last years. It is the purpose of this paper to prove exact estimates between the approximations obtained via this system and solutions of the original physical system. Although the three-wave interaction model is believed to describe a number of different physical models we restrict attention to its application as a model of the resonant interaction of water waves subject to weak surface tension.

Type
Papers
Copyright
© 2003 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)
9
Cited by

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Estimates for the three-wave interaction of surface water waves
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

Estimates for the three-wave interaction of surface water waves
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

Estimates for the three-wave interaction of surface water waves
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *