Asymptotic Behavior of Solutions of Equations of Main Resonance |
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Authors: | Kalyakin L. A. |
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Affiliation: | (1) Ufa Scientific Center, RAS, Mathematical Institute, Ufa, Russia |
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Abstract: | We investigate a system of two first-order differential equations that appears when averaging nonlinear systems over fast one-frequency oscillations. The main result is the asymptotic behavior of a two-parameter family of solutions with an infinitely growing amplitude. In addition, we find the asymptotic behavior of another two-parameter family of solutions with a bounded amplitude. In particular, these results provide the key to understanding autoresonance as the phenomenon of a considerable growth of forced nonlinear oscillations initiated by a small external pumping. |
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Keywords: | nonlinear equations asymptotic behavior WKB approximation |
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