(Non)linear instability of periodic traveling waves: Klein-Gordon and KdV type equations

Pava, Jaime Angulo; Natali, Fabio

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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

(Non)linear instability of periodic traveling waves: Klein-Gordon and KdV type equations

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Author(s):	Pava, Jaime Angulo ^[1] ; Natali, Fabio ^[2] Total Authors: 2
Affiliation:	^[1] IME USP, Dept Math, BR-05508090 Sao Paulo - Brazil ^[2] DMA UEM, Dept Math, BR-87020900 Maringa, Parana - Brazil Total Affiliations: 2
Document type:	Journal article
Source:	ADVANCES IN NONLINEAR ANALYSIS; v. 3, n. 2, p. 95-123, MAY 2014.
Web of Science Citations:	6
Abstract
We prove the existence and nonlinear instability of periodic traveling wave solutions for the critical one-dimensional Klein-Gordon equation. We also establish a linear instability criterium for a KdV type system. An application of this approach is made to obtain the linear/nonlinear instability of vector cnoidal wave profiles. Finally, via a theoretical and numerical approach we show the linear stability or instability of periodic positive and sign changing waves, respectively, for the critical Korteweg-de Vries equation. (AU)

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