38 citations · 84 across the 11 of their papers we have counts for
15 papers
Interface problems of mixed spatial order
Dionyssios Mantzavinos, Ravindra Pethiyagoda, Dave Smith
We solve interface problems on the line between various constant coefficient linear evolution partial differential equations. Our prototypical examples are the heat, linear Schrödi…
The Airy equation with nonlocal conditions
Bekzod Normatov, David Andrew Smith
We study a third order dispersive linear evolution equation on the finite interval subject to an initial condition and inhomogeneous boundary conditions but, in place of one of the…
Fokas diagonalization of piecewise constant coefficient linear differential operators on finite intervals and networks
Sultan Aitzhan, Sambhav Bhandari, David Andrew Smith
We describe a new form of diagonalization for linear two point constant coefficient differential operators with arbitrary linear boundary conditions. Although the diagonalization i…
New Revival Phenomena for Linear Integro-Differential Equations
Lyonell Boulton, Peter J. Olver, Beatrice Pelloni +1
We present and analyse a novel manifestation of the revival phenomenon for linear spatially periodic evolution equations, in the concrete case of three nonlocal equations that aris…
Linear Dispersive Shocks
David Smith, Thomas Trogdon, Vishal Vasan
We present a linear dispersive partial differential equation which manifests a number of qualitative features of dispersive shocks, typically thought to occur only in nonlinear mod…
Revivals and Fractalisation in the Linear Free Space Schrödinger Equation
Peter J Olver, Natalie E Sheils, David A Smith
We consider the one-dimensional linear free space Schrödinger equation on a bounded interval subject to homogeneous linear boundary conditions. We prove that, in the case of pseudo…