On the existence and evaluation of Stokes phenomena in fluid mechanics

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.