Strong instability of solitary waves for nonlinear Klein–Gordon equations and generalized Boussinesq equations Instabilité forte d’ondes solitaires pour des équations de Klein–Gordon non linéaires et des équations généralisées de Boussinesq
نویسندگان
چکیده
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. © 2006 Elsevier Masson SAS. All rights reserved. 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 nonlinéarité. © 2006 Elsevier Masson SAS. All rights reserved. MSC: 35L70; 35A15; 35B35; 35R25
منابع مشابه
Strong instability of solitary waves for nonlinear Klein-Gordon equations and generalized Boussinesq equations
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.
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