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math.AP2021★ 14 cited
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…
math.AP2020
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…
math.AP2011
The Kadomtsev-Petviashvili I Equation on the Half-Plane
Dionyssios Mantzavinos, Athanassios S. Fokas
A new method for the solution of initial-boundary value problems for \textit{linear} and \textit{integrable nonlinear} evolution PDEs in one spatial dimension was introduced by one…