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IMA Journal of Applied Mathematics 1968 4(3):282-294; doi:10.1093/imamat/4.3.282
© 1968 by Institute of Mathematics and its Applications
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Resonance in Almost Linear Systems

H. C. LEVEY and J. J. MAHONY {dagger}

Department of Mathematics, University of Western Australia

Estimates, useful for all times, are sought for the resonant response of a system with small non-linearity. It is shown that the method of multiple scales can be used to generate a representation which is formally asymptotic at all times and over a significant time interval is a valid approximation to some solution of the system. It is shown, by example, that this estimate is not always a useful representation of any one solution for all time. Plausible arguments are given that the approximation is nevertheless useful for the determination of the behaviour of a physical system if not of the pathological solutions of the differential equations which may represent it.


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