Boundary value problems for integrable nonlinear evolution PDEs formulated on the half-
line can be analyzed by the unified method introduced by one of the authors and used …

In this paper, we consider the solution to the linear Korteweg‐De Vries (KdV) equation, both
homogeneous and forced, on the quadrant x∈ R+, t∈ R+ {x∈R^+,t∈R^+} via the unified …

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 …

Every applied mathematician has used separation of variables. For a given boundary value
problem (BVP) in two dimensions, the starting point of this powerful method is the separation …

We derive the solution of the one-dimensional wave equation for the Dirichlet and Robin
initial-boundary value problems (IBVPs) formulated on the half line and the finite interval …

Recent work has given rise to a novel and simple numerical technique for solving elliptic
boundary value problems formulated in convex polygons in two dimensions. The method …

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 …

A new general transform method for the solution of mixed boundary value problems (BVPs)
for Laplace's equation in multiply connected circular domains is formulated. Circular …

We analyse the Dirichlet problem for the elliptic sine-Gordon equation in the upper half
plane. We express the solution q (x, y) in terms of a Riemann–Hilbert problem whose jump …

We provide the first significant extension of the unified transform (also known as the Fokas
method) applied to elliptic boundary value problems, namely, we extend the method to …