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Type: Artigo de periódico
Title: On The Instability Of Solitary Waves Solutions Of The Generalized Benjamin Equation
Author: Pava J.A.
Abstract: This work is concerned with instability properties of solutions u(x, t) = φ(x -ct) of the equation ut + (up)x + lHuxx + uxxx = 0 in R, where p ε ℕ, p ≥ 2, and H is the Hilbert transform. Here, π will be a solution of the pseudo-differential equation π'' + lHπ'-cπ =-πp solving a certain variational problem. We prove that the set ωφ = {π(· + y): y ε ℝ } is unstable by the flow of the evolution equation above provided l is small, c > 1/4l2 and p ≥ 5. Moreover, the trajectories used to exhibit instability are global and uniformly bounded. Finally, we extend these results for a natural generalization of the evolution equation above with general forms of competing dispersion, in particular, we obtain instability results for some Korteweg-de Vries type equations without requiring spectral conditions.
Rights: fechado
Identifier DOI: 
Date Issue: 2003
Appears in Collections:Unicamp - Artigos e Outros Documentos

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