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|Type:||Artigo de periódico|
|Title:||On The Instability Of Solitary-wave Solutions For Fifth-order Water Wave Models|
|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 the trajectories used to exhibit instability will be uniformly bounded in H2(ℝ).|
|Appears in Collections:||Unicamp - Artigos e Outros Documentos|
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