File Download

There are no files associated with this item.

  Links for fulltext
     (May Require Subscription)
Supplementary

Article: Employing the dynamics of poles in the complex plane to describe properties of rogue waves: case studies using the Boussinesq and complex modified Korteweg–de Vries equations

TitleEmploying the dynamics of poles in the complex plane to describe properties of rogue waves: case studies using the Boussinesq and complex modified Korteweg–de Vries equations
Authors
KeywordsDynamics
Equations of motion
Nonlinear equations
Poles
Water waves
Issue Date2020
PublisherSpringer Verlag Dordrecht. The Journal's web site is located at http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0924-090X
Citation
Nonlinear Dynamics, 2020, v. 99 n. 4, p. 2961-2970 How to Cite?
AbstractThe dynamics and properties of rogue waves of two classical evolution equations are studied in terms of trajectories of the poles of the exact solutions, by analytically continuing the spatial variable to be complex. The Boussinesq equation describes the motion of hydrodynamic waves in two opposite directions in the shallow water regime. The complex modified Korteweg–de Vries equation is relevant for wave packets in nonlinear media governed by a higher-order nonlinear Schrödinger equation, for the special case where second-order dispersion and cubic self-interaction are absent. On examining the movement of poles of the exact solutions for rogue waves, the real parts of the poles correlate well with the locations of maximum displacements in the physical space. This phenomenon holds for high precision numerically for the first-, second- and third-order rogue waves of the Boussinesq equation. A similar principle is also valid for the first- and second-order rogue waves of the complex modified Korteweg–de Vries equation. The imaginary parts of the poles can generate useful information too. For these two evolution models, a smaller imaginary part in the complex plane is associated with a larger amplitude of the rogue wave in physical space. An empirical formula is proposed which works well for the three lowest orders of rogue waves of the Boussinesq equation.
Persistent Identifierhttp://hdl.handle.net/10722/283373
ISSN
2020 Impact Factor: 5.022
2015 SCImago Journal Rankings: 1.511
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorCHUNG, WC-
dc.contributor.authorCHIU, TL-
dc.contributor.authorChow, KW-
dc.date.accessioned2020-06-22T02:55:38Z-
dc.date.available2020-06-22T02:55:38Z-
dc.date.issued2020-
dc.identifier.citationNonlinear Dynamics, 2020, v. 99 n. 4, p. 2961-2970-
dc.identifier.issn0924-090X-
dc.identifier.urihttp://hdl.handle.net/10722/283373-
dc.description.abstractThe dynamics and properties of rogue waves of two classical evolution equations are studied in terms of trajectories of the poles of the exact solutions, by analytically continuing the spatial variable to be complex. The Boussinesq equation describes the motion of hydrodynamic waves in two opposite directions in the shallow water regime. The complex modified Korteweg–de Vries equation is relevant for wave packets in nonlinear media governed by a higher-order nonlinear Schrödinger equation, for the special case where second-order dispersion and cubic self-interaction are absent. On examining the movement of poles of the exact solutions for rogue waves, the real parts of the poles correlate well with the locations of maximum displacements in the physical space. This phenomenon holds for high precision numerically for the first-, second- and third-order rogue waves of the Boussinesq equation. A similar principle is also valid for the first- and second-order rogue waves of the complex modified Korteweg–de Vries equation. The imaginary parts of the poles can generate useful information too. For these two evolution models, a smaller imaginary part in the complex plane is associated with a larger amplitude of the rogue wave in physical space. An empirical formula is proposed which works well for the three lowest orders of rogue waves of the Boussinesq equation.-
dc.languageeng-
dc.publisherSpringer Verlag Dordrecht. The Journal's web site is located at http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0924-090X-
dc.relation.ispartofNonlinear Dynamics-
dc.rightsThis is a post-peer-review, pre-copyedit version of an article published in [insert journal title]. The final authenticated version is available online at: http://dx.doi.org/[insert DOI]-
dc.subjectDynamics-
dc.subjectEquations of motion-
dc.subjectNonlinear equations-
dc.subjectPoles-
dc.subjectWater waves-
dc.titleEmploying the dynamics of poles in the complex plane to describe properties of rogue waves: case studies using the Boussinesq and complex modified Korteweg–de Vries equations-
dc.typeArticle-
dc.identifier.emailChow, KW: kwchow@hku.hk-
dc.identifier.authorityChow, KW=rp00112-
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1007/s11071-020-05475-z-
dc.identifier.scopuseid_2-s2.0-85078239508-
dc.identifier.hkuros310411-
dc.identifier.volume99-
dc.identifier.issue4-
dc.identifier.spage2961-
dc.identifier.epage2970-
dc.identifier.isiWOS:000524454800027-
dc.publisher.placeNetherlands-
dc.identifier.issnl0924-090X-

Export via OAI-PMH Interface in XML Formats


OR


Export to Other Non-XML Formats