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dc.contributor.authorAngulo Pava, Jaime ( Orcid Icon 0000-0002-7453-1782 )
dc.date.accessioned2020-09-10T19:52:50Z
dc.date.available2020-09-10T19:52:50Z
dc.date.issued2003-01-10
dc.identifier.citationAngulo Pava, J. (2003). On the instability of solitary-wave solutions for fifth-order water wave models. Electronic Journal of Differential Equations, 2003(06), pp. 1-18.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/12573
dc.description.abstract

This work presents new results about the instability of solitary-wave solutions to a generalized fifth-order Korteweg-deVries equation of the form

ut + uxxxxx + buxxx = (G(u, ux, uxx))x,

where G(q, r, s) = Fq(q, r) - rFqr(q, r) - sFrr(q, r) for some F(q, r) which is homogeneous of degree p + 1 for some p > 1. This model arises, for example, in the mathematical description of phenomena in water waves and magneto-sound propagation in plasma. The existence of a class of solitary-wave solutions is obtained by solving a constrained minimization problem in H2(ℝ) which is based in results obtained by Levandosky. The instability of this class of solitary-wave solutions is determined for b ≠ 0, and it is obtained by making use of the variational characterization of the solitary waves and a modification of the theories of instability established by Shatah & Strauss, Bona & Souganidis & Strauss and Gonçalves Ribeiro. Moreover, our approach shows that trajectories used to exhibit instability will be uniformly bounded in H2(ℝ).

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dc.formatText
dc.format.extent18 pages
dc.format.medium1 file (.pdf)
dc.language.isoenen_US
dc.publisherSouthwest Texas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2003, San Marcos, Texas: Southwest Texas State University and University of North Texas.
dc.subjectWater wave modelen_US
dc.subjectVariational methodsen_US
dc.subjectSolitary wavesen_US
dc.subjectInstabilityen_US
dc.titleOn the Instability of Solitary-wave Solutions for Fifth-order Water Wave Modelsen_US
dc.typepublishedVersion
txstate.documenttypeArticle
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.


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