On the Instability of Solitary-wave Solutions for Fifth-order Water Wave Models
| dc.contributor.author | Angulo Pava, Jaime | |
| dc.date.accessioned | 2020-09-10T19:52:50Z | |
| dc.date.available | 2020-09-10T19:52:50Z | |
| dc.date.issued | 2003-01-10 | |
| 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). | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 18 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Angulo Pava, J. (2003). On the instability of solitary-wave solutions for fifth-order water wave models. <i>Electronic Journal of Differential Equations, 2003</i>(06), pp. 1-18. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/12573 | |
| dc.language.iso | en | |
| dc.publisher | Southwest Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| 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 | |
| dc.subject | Variational methods | |
| dc.subject | Solitary waves | |
| dc.subject | Instability | |
| dc.title | On the Instability of Solitary-wave Solutions for Fifth-order Water Wave Models | |
| dc.type | Article |