398 citations · 1k across the 31 of their papers we have counts for
32 papers
A complex spatial frequency approach to optimal control of finite-extent linear evolution systems
Zhexian Li, Athanassios S. Fokas, Ketan Savla
We consider the linear quadratic regulator (LQR) for one-dimensional linear evolution partial differential equations (PDEs) on a finite interval in space. The control is applied as…
The implementation of the unified transform to the nonlinear Schrödinger equation with periodic initial conditions
B. Deconinck, A. S. Fokas, J. Lenells
The unified transform method (UTM) provides a novel approach to the analysis of initial-boundary value problems for linear as well as for a particular class of nonlinear partial di…
A new approach to integrable evolution equations on the circle
A. S. Fokas, J. Lenells
We propose a new approach for the solution of initial value problems for integrable evolution equations in the periodic setting based on the unified transform. Using the nonlinear…
Linearizable boundary value problems for the elliptic sine-Gordon and the elliptic Ernst equations
J. Lenells, A. S. Fokas
By employing a novel generalization of the inverse scattering transform method known as the unified transform or Fokas method, it can be shown that the solution of certain physical…
Fokas method for linear boundary value problems involving mixed spatial derivatives
Ahmet Batal, Athanassios S. Fokas, Türker Özsarı
We obtain solution representation formulas for some linear initial boundary value problems posed on the half space that involve mixed spatial derivative terms via the unified trans…
A hybrid analytical-numerical algorithm for determining the neuronal current via EEG
Parham Hashemzadeh, A. S. Fokas, C. B. Schönlieb
In this study, the neuronal current in the brain is represented using Helmholtz decomposition. It was shown in earlier work that data obtained via electroencephalography (EEG) are…