Exponential Asymptotics and Stokes Line Smoothing for Generalized Solitary Waves
arXiv:1410.4124 · doi:10.1007/978-3-7091-0408-8_4
Abstract
In a companion paper, Grimshaw (Asymptotic Methods in Fluid Mechanics, 2010, pp. 71-120) has demonstrated how techniques of Borel summation can be used to elucidate the exponentially small terms that lie hidden beyond all orders of a divergent asymptotic expansion. Here, we provide an alternative derivation of the generalized solitary waves of the fifth-order Korteweg-de Vries equation. We will first optimally truncate the asymptotic series, and then smooth the Stokes line. Our method provides an explicit view of the switching-on mechanism, and thus increased understanding of the Stokes Phenomenon.
arXiv commentPre-print version used for publication, but with small additions (e.g. self-contained bibliography)
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