On the Instability of Solitary-wave Solutions for Fifth-order Water Wave Models
|dc.contributor.author||Angulo Pava, Jaime ( 0000-0002-7453-1782 )|
|dc.identifier.citation||Angulo 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.medium||1 file (.pdf)|
|dc.publisher||Southwest Texas State University, Department of Mathematics||en_US|
|dc.source||Electronic Journal of Differential Equations, 2003, San Marcos, Texas: Southwest Texas State University and University of North Texas.|
|dc.subject||Water wave model||en_US|
|dc.title||On the Instability of Solitary-wave Solutions for Fifth-order Water Wave Models||en_US|
This work is licensed under a Creative Commons Attribution 4.0 International License.