4 papers
On the stability of large-amplitude gravity-capillary surface waves
Josh Shelton, Adam Rook
We consider the stability of periodic gravity-capillary waves of finite amplitude for small values of the surface tension. Linear stability with respect to both superharmonic and s…
Automorphisms of Stokes multipliers in higher-order WKBJ theory
Josh Shelton, Samuel Crew, Christopher J. Lustri
We consider the Stokes phenomenon and higher-order Stokes phenomenon (HOSP) of formal asymptotic transseries arising in the WKBJ analysis of linear differential equations and integ…
Time-dependent nonlinear gravity-capillary surface waves with viscous dissipation and wind forcing
Josh Shelton, Paul Milewski, Philippe H. Trinh
We develop a time-dependent conformal method to study the effect of viscosity on steep surface waves. When the effect of surface tension is included, numerical solutions are found…
Exponential asymptotics and higher-order Stokes phenomenon in singularly perturbed ODEs
Josh Shelton, Samuel Crew, Philippe H. Trinh
The higher-order Stokes phenomenon can emerge in the asymptotic analysis of many problems governed by singular perturbations. Indeed, over the last two decades, the phenomena has a…