We study initial boundary value problems for linear scalar partial differential equations with constant coefficients, with spatial derivatives of arbitrary order, posed on the domain {t > 0, 0 < x <â€¦ (More)

We use a spectral method to solve numerically two nonlocal, nonlinear, dispersive, integrable wave equations, the Benjamin-Ono and the Intermediate Long Wave equations. The proposed numerical methodâ€¦ (More)

We use a spectral transform method to study general boundary-value problems for thirdorder, linear, evolution partial differential equations with constant coefficients, posed on a finite spaceâ€¦ (More)

The problem of heat conduction in one-dimensional piecewise homogeneous composite materials is examined by providing an explicit solution of the one-dimensional heat equation in each domain. Theâ€¦ (More)

We study boundary value problems posed in a semistrip for the elliptic sine-Gordon equation, which is the paradigm of an elliptic integrable PDE in two variables. We use the method introduced by oneâ€¦ (More)

We present an algorithm for characterising the generalised Dirichlet to Neumann map for moving initial-boundary value problems. This algorithm is derived by combining the so-called global relation,â€¦ (More)

We implement several numerical methods for computing the solution of the Cauchy problems for two wellknown integrable equations in two space dimensions, known as the Daveyâ€“Stewartson I and IIâ€¦ (More)

This article presents an overview of a transform method for solving linear and integrable nonlinear partial differential equations. This new transform method, proposed by Fokas, yields aâ€¦ (More)