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

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.

Object Details

• Location: Deutsche Nationalbibliothek Frankfurt am Main
• Extent: Online-Ressource
• Language: Englisch

References and Relationships

• Bibliographic citation: (Non) linear instability of periodic traveling waves: Klein–Gordon and KdV type equations ; volume:3 ; number:2 ; year:2014 ; pages:95-123 ; extent:29 ; Advances in nonlinear analysis ; 3, Heft 2 (2014), 95-123 (gesamt 29)

Contributors, Places and Time

• Creator: Angulo Pava, Jaime ; Natali, Fabio

Further information

• DOI: 10.1515/anona-2014-0008
• URN: urn:nbn:de:101:1-2405011749457.269894984313
• Rights: Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
• Last update: 14.08.2025, 11:02 AM CEST