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Book Chapter: Modulational instability and rogue waves in shallow water models

TitleModulational instability and rogue waves in shallow water models
Authors
Issue Date2016
PublisherSpringer International Publishing
Citation
Modulational instability and rogue waves in shallow water models. In Tobisch, E (Ed.), New Approaches to Nonlinear Waves, p. 135-151. Cham: Springer International Publishing, 2016 How to Cite?
AbstractIt is now well known that the focussing nonlinear Schrödinger equation allows plane waves to be modulationally unstable, and at the same time supports breather solutions which are often invoked as models for rogue waves. This suggests a direct connection between modulation instability and the existence of rogue waves. In this chapter we review this connection for a suite of long wave models, such as the Korteweg-de Vries equation, the extended Korteweg-de Vries (Gardner) equation, often used to describe surface and internal waves in shallow water, a Boussinesq equation and, also a coupled set of Korteweg-de Vries equations.
Persistent Identifierhttp://hdl.handle.net/10722/234313
ISBN

 

DC FieldValueLanguage
dc.contributor.authorGrimshaw, R-
dc.contributor.authorChow, KW-
dc.contributor.authorChan, HN-
dc.date.accessioned2016-10-14T07:00:30Z-
dc.date.available2016-10-14T07:00:30Z-
dc.date.issued2016-
dc.identifier.citationModulational instability and rogue waves in shallow water models. In Tobisch, E (Ed.), New Approaches to Nonlinear Waves, p. 135-151. Cham: Springer International Publishing, 2016-
dc.identifier.isbn9783319206899-
dc.identifier.urihttp://hdl.handle.net/10722/234313-
dc.description.abstractIt is now well known that the focussing nonlinear Schrödinger equation allows plane waves to be modulationally unstable, and at the same time supports breather solutions which are often invoked as models for rogue waves. This suggests a direct connection between modulation instability and the existence of rogue waves. In this chapter we review this connection for a suite of long wave models, such as the Korteweg-de Vries equation, the extended Korteweg-de Vries (Gardner) equation, often used to describe surface and internal waves in shallow water, a Boussinesq equation and, also a coupled set of Korteweg-de Vries equations.-
dc.languageeng-
dc.publisherSpringer International Publishing-
dc.relation.ispartofNew Approaches to Nonlinear Waves-
dc.titleModulational instability and rogue waves in shallow water models-
dc.typeBook_Chapter-
dc.identifier.emailChow, KW: kwchow@hku.hk-
dc.identifier.authorityChow, KW=rp00112-
dc.identifier.doi10.1007/978-3-319-20690-5_5-
dc.identifier.hkuros267324-
dc.identifier.spage135-
dc.identifier.epage151-
dc.publisher.placeCham-

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