JournalsaihpcVol. 24, No. 4pp. 539–548

Strong instability of solitary waves for nonlinear Klein–Gordon equations and generalized Boussinesq equations

  • Yue Liu

    Department of Mathematics, University of Texas, Arlington, TX 76019, USA

  • Masahito Ohta

    Department of Mathematics, Faculty of Science, Saitama University, Saitama 338-8570, Japan

  • Grozdena Todorova

    Department of Mathematics, University of Tennessee, Knoxville, TN 37996, USA
Strong instability of solitary waves for nonlinear Klein–Gordon equations and generalized Boussinesq equations cover
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Abstract

We study here instability problems of standing waves for the nonlinear Klein–Gordon equations and solitary waves for the generalized Boussinesq equations. It is shown that those special wave solutions may be strongly unstable by blowup in finite time, depending on the range of the wave's frequency or the wave's speed of propagation and on the nonlinearity.

Résumé

On étudie des problèmes d'instabilité des ondes stationnaires pour des équations de Klein–Gordon non linéaires et des ondes solitaires pour des équations généralisées de Boussinesq. On établit que ces solutions d'ondes spéciales peuvent être fortement instables par explosion en temps fini, selon le rang de la fréquence des ondes ou la vitesse de propagation des ondes et la non-linéarité.

Cite this article

Yue Liu, Masahito Ohta, Grozdena Todorova, Strong instability of solitary waves for nonlinear Klein–Gordon equations and generalized Boussinesq equations. Ann. Inst. H. Poincaré Anal. Non Linéaire 24 (2007), no. 4, pp. 539–548

DOI 10.1016/J.ANIHPC.2006.03.005