Strong instability of solitary waves for nonlinear Klein–Gordon equations and generalized Boussinesq equations |
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| Authors: | Yue Liu Masahito Ohta Grozdena Todorova |
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| Institution: | 1. Department of Mathematics, University of Texas, Arlington, TX 76019, USA;2. Department of Mathematics, Faculty of Science, Saitama University, Saitama 338-8570, Japan;3. Department of Mathematics, University of Tennessee, Knoxville, TN 37996, USA |
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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. |
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| Keywords: | 35L70 35A15 35B35 35R25 |
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