Abstract
The perturbation strategy known as the “method of multiple scales” lies at the heart of solitary wave theory. First, it is the vehicle by which three-dimensional reality is approximated by one-dimensional models such as the Korteweg-deVries equation. One might call this “reduction of dimension”. Second, it can be applied within the microworld of one-dimensional wave equations to generate further approximations, such as FKdV ∈-series in which the lowest order is the KdV solitary wave.
“about the present title [Divergent Series], now colourless, there hung an aroma of paradox and audacity.” — Sir John E. Littlewood, (preface to Hardy, 1949)
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© 1998 Springer Science+Business Media Dordrecht
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Boyd, J.P. (1998). The Method of Multiple Scales and the ∈-Power Series. In: Weakly Nonlocal Solitary Waves and Beyond-All-Orders Asymptotics. Mathematics and Its Applications, vol 442. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-5825-5_2
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DOI: https://doi.org/10.1007/978-1-4615-5825-5_2
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