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 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 …

We establish local well‐posedness in the sense of Hadamard for a certain third‐order
nonlinear Schrödinger equation with a multiterm linear part and a general power …

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 …

The well-posedness of the initial–boundary value problem (ibvp) for the Korteweg–de Vries
equation on the half-line is studied for initial data u 0 (x) in spatial Sobolev spaces H s (0,∞) …

The initial-boundary value problem (ibvp) for the m-th order dispersion Korteweg-de Vries
(KdV) equation on the half-line with rough data and solution in restricted Bourgain spaces is …

Abstract The asymptotic Dirichlet‐to‐Neumann (D‐N) map is constructed for a class of
scalar, constant coefficient, linear, third‐order, dispersive equations with asymptotically …

This paper addresses the impact of the presence of a boundary memory term in the third-
order Korteweg–de Vries equation in a bounded interval 0, ℓ 0, ℓ. First, an overall literature …

In this note, we give an elementary proof of the lack of null controllability for the heat
equation on the half line by employing the machinery inherited by the unified transform …

The initial-boundary value problem for the nonlinear Schrödinger equation on the half-line
with initial data in Sobolev spaces H s (0,∞), 1/2< s⩽ 5/2, s≠ 3/2, and Robin boundary data …