The primary objective of this investigation revolves around scrutinizing the generalized
Kawahara equation, a consequential nonlinear evolution equation prevalent in diverse …

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 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 paper, the main work is to study the N-soliton solutions for the nonlocal Fokas–Lenells
equation. Then, the matrix Riemann–Hilbert problem is constructed for this nonlocal system …

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 …

We study the local and global wellposedness of the initial-boundary value problem for the
biharmonic Schr\" odinger equation on the half-line with inhomogeneous Dirichlet-Neumann …

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 …

We define and study the Airy operator on star graphs. The Airy operator is a third-order
differential operator arising in different contexts, but our main concern is related to its role as …