In this paper, we report on the discovery of a previously-unknown type of long-range
instability phenomenon for the one-dimensional linear Schrödinger (LS) equation on the …

In this review I summarize some of the most significant advances of the last decade in the
analysis and solution of boundary value problems for integrable partial differential equations …

A novel method is presented for explicitly solving inhomogeneous initial-boundary-value
problems (IBVPs) on the half-line for a well-known coupled system of evolution partial …

This paper employs the unified transform, also known as the Fokas method, to solve the
advection-dispersion equation on the half-line. This method combines complex analysis with …

The initial‐boundary value problem for the heat equation on x> 0, t> 0\left {x> 0, t>
0\right\} with nonzero Dirichlet boundary data is studied rigorously, with emphasis on the …

This paper elaborates on a new approach for solving the generalized Dirichlet‐to‐Neumann
map, in the large time limit, for linear evolution PDEs formulated on the half‐line with time …

This article presents a new numerical method, which approximates Neumann type null
controls for the heat equation and is based on the Fokas method. This is a direct method for …

We study the inhomogeneous Airy partial differential equation (also called Stokes or
linearized Korteweg-de Vries equation with a negative sign) on the half-line with generic …

In this paper, we announce a rigorous approach to establishing uniqueness results, under
certain conditions, for initial-boundary-value problems for a class of linear evolution partial …

We derive the solution representation for a large class of nonlocal boundary value problems
for linear evolution partial differential equations (PDE) with constant coefficients in one …