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arXiv · 1410.4124

Exponential Asymptotics and Stokes Line Smoothing for Generalized Solitary Waves

Philippe H. Trinh
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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.

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BibTeXRIS

Philippe H. Trinh. 2014-10-08. Exponential Asymptotics and Stokes Line Smoothing for Generalized Solitary Waves. https://doi.org/10.1007/978-3-7091-0408-8_4

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