We characterize the long‐time asymptotic behavior of the focusing nonlinear Schrödinger
(NLS) equation on the line with symmetric, nonzero boundary conditions at infinity by using …

In this review paper, we discuss some of our recent results concerning the rigorous analysis
of initial boundary value problems (IBVPs) and newly discovered effects for certain evolution …

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 …

Nonlinear Systems and Their Remarkable Mathematical Structures, Volume 1 aims to
describe the recent progress in nonlinear differential equations and nonlinear dynamical …

In this work, a matrix Riemann–Hilbert problem of a mixed Chen–Lee–Liu derivative
nonlinear Schrödinger (CLL-NLS in brief) equation on the half-line is established by 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 …

The question of whether features and behaviors that are characteristic to completely
integrable systems persist in the transition to non-integrable settings is a central one in the …

Considered here is a class of Boussinesq systems of Nwogu type. Such systems describe
propagation of nonlinear and dispersive water waves of significant interest such as solitary …

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 …