35 citations · 94 across the 7 of their papers we have counts for
4 papers · 1 filter
Dispersive Lamb Systems
Peter Olver, Natalie Sheils
Under periodic boundary conditions, a one-dimensional dispersive medium driven by a Lamb oscillator exhibits a smooth response when the dispersion relation is asymptotically linear…
The time-dependent Schrödinger equation with piecewise constant potentials
Natalie E Sheils, Bernard Deconinck
The linear Schrödinger equation with piecewise constant potential in one spatial dimension is a well-studied textbook problem. It is one of only a few solvable models in quantum me…
The Linear KdV Equation with an Interface
Bernard Deconinck, Natalie E. Sheils, David A. Smith
The interface problem for the linear Korteweg-de Vries (KdV) equation in one-dimensional piecewise homogeneous domains is examined by constructing an explicit solution in each doma…
Heat equation on a network using the Fokas method
N. E. Sheils, D. A. Smith
The problem of heat conduction on networks of multiply connected rods is solved by providing an explicit solution of the one-dimensional heat equation in each domain. The size and…