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Strong instability of solitary waves for nonlinear Klein-Gordon equations and generalized Boussinesq equations. (English) Zbl 1120.35013
Summary: 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 blow-up in finite time, depending on the range of the wave’s frequency or the wave’s speed of propagation and on the nonlinearity.

MSC:
35B35 Stability in context of PDEs
35R25 Ill-posed problems for PDEs
35L70 Second-order nonlinear hyperbolic equations
35A15 Variational methods applied to PDEs
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