4 papers
A caustic terminating at an inflection point
J. R. Ockendon, H. Ockendon, R. H. Tew +2
We present an asymptotic and numerical study of the evolution of an incoming wavefield which has a caustic close to a curve with an inflection point. Our results reveal the emergen…
Contour integral solutions of the parabolic wave equation
David P. Hewett, John R. Ockendon, Valery P. Smyshlyaev
We present a simple systematic construction and analysis of solutions of the two-dimensional parabolic wave equation that exhibit far-field localisation near a given algebraic plan…
Interactions of point vortices in the Zabusky-McWilliams model with a background flow
Colm Connaughton, John R. Ockendon
We combine a simple quasi-geostrophic flow model with the Zabusky-McWilliams theory of atmospheric vortex dynamics to address a hurricane-tracking problem of interest to the insura…
On bounded solutions of the balanced generalized pantograph equation
Leonid Bogachev, Gregory Derfel, Stanislav Molchanov +1
The question about the existence and characterization of bounded solutions to linear functional-differential equations with both advanced and delayed arguments was posed in early 1…