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dc.contributor.authorAngulo Pava, Jaime ( Orcid Icon 0000-0002-7453-1782 )
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

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).

dc.format.extent18 pages
dc.format.medium1 file (.pdf)
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.titleOn the Instability of Solitary-wave Solutions for Fifth-order Water Wave Modelsen_US
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.



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