Geodesic
Asymptotic Behavior of Solutions of Equations of Main Resonance
Teoretičeskaâ i matematičeskaâ fizika, Tome 137 (2003) no. 1, pp. 142-152

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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.
Keywords: nonlinear equations, asymptotic behavior, WKB approximation. 
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     author = {L. A. Kalyakin},
     title = {Asymptotic {Behavior} of {Solutions} of {Equations} of {Main} {Resonance}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     url = {http://geodesic.mathdoc.fr/item/TMF_2003_137_1_a14/}
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L. A. Kalyakin. Asymptotic Behavior of Solutions of Equations of Main Resonance. Teoretičeskaâ i matematičeskaâ fizika, Tome 137 (2003) no. 1, pp. 142-152. http://geodesic.mathdoc.fr/item/TMF_2003_137_1_a14/