Exponential Asymptotics and Stokes Line Smoothing for Generalized Solitary Waves

摘要

In a companion paper, Grimshaw (Asymptotic Methods in Fluid Mechanics, 2010,pp. 71-120) has demonstrated how techniques of Borel summation can be used toelucidate the exponentially small terms that lie hidden beyond all orders of adivergent asymptotic expansion. Here, we provide an alternative derivation ofthe generalized solitary waves of the fifth-order Korteweg-de Vries equation.We will first optimally truncate the asymptotic series, and then smooth theStokes line. Our method provides an explicit view of the switching-onmechanism, and thus increased understanding of the Stokes Phenomenon.