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 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 …

We consider the initial-boundary value problem of the nonlinear Schrödinger equation on
the half line with a nonlinear Neumann boundary condition. After establishing the boundary …

We study the Cauchy problem for the defocusing nonlinear Schr\" odinger (NLS) equation
under the assumption that the solution vanishes as $ x\to+\infty $ and approaches an …

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 …

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 …

This work studies the initial-boundary value problem (ibvp) of the two-dimensional nonlinear
Schrödinger equation on the half-plane with initial data in Sobolev spaces and Neumann or …

The well-posedness of the Neumann and Robin problems for the Korteweg–de Vries
equation is studied with data in Sobolev spaces. Using the Fokas unified transform method …

We implement the numerical inverse scattering transform (NIST) for the sine-Gordon
equation in laboratory coordinates on the real line using the method developed by Trogdon …