On the existence and evaluation of Stokes phenomena in fluid mechanics

Article type: Research Article

Authors: Alexandrakis, Nik^{; *}

Affiliations: Department of Mathematics and Statistics, Lancaster University, UK. E-mail: n.alexandrakis@lancaster.ac.uk

Correspondence: [*] Corresponding author. E-mail: n.alexandrakis@lancaster.ac.uk.

Abstract: A singularly perturbed, high order KdV-type model, which describes localized travelling waves (“solitons”) is being considered. We focus on the Inner solution, and detect Stokes phenomena that are crucial as to whether we can obtain a suitable solution. We provide a simple proof that the corresponding Stokes constant is non-zero. Also, we evaluate this splitting constant numerically by using two methods that are induced by the underlying theory.

Keywords: Stokes phenomenon, Stokes constants, Exponentially small splitting of Separatrices

DOI: 10.3233/ASY-211723

Journal: Asymptotic Analysis, vol. 129, no. 1, pp. 113-139, 2022