5 papers
Linearizable Initial-Boundary Value Problems for the sine-Gordon Equation on the Half-Line
A. S. Fokas
A rigorous methodology for the analysis of initial boundary value problems on the half-line, , , for integrable nonlinear evolution PDEs has recently appeared in t…
The Davey-Stewartson I Equation on the Quarter Plane with Homogeneous Dirichlet Boundary Conditions
A. S. Fokas
Dromions are exponentially localised coherent structures supported by nonlinear integrable evolution equations in two spatial dimensions.In the study of initial-value problems on t…
A Generalization of both the Method of Images and of the Classical Integral Transforms
Athanassios S. Fokas, Daniel ben-Avraham
A new method for the solution of initial-boundary value problems for evolution PDEs recently introduced by Fokas is generalised to multidimensions. Also the relation of this method…
The Inverse Spectral Theory for the Ward Equation and for the 2+1 Chiral Model
A. S. Fokas, T. A. Ioannidou
We solve the Cauchy problem of the Ward model in light-cone coordinates using the inverse spectral (scattering) method. In particular we show that the solution can be constructed b…
Nonlinear Integrable Equations and Nonlinear Fourier Transform
A. S. Fokas, I. M. Gelfand, M. V. Zyskin
In the paper we study nonlocal functionals whose kernels are homogeneous generalized functions. We also use such functionals to solve the Korteweg-de Vries , the nonlinear Schrödin…