The present survey is devoted to a general group-theoretic scheme which allows to
construct integrable Hamiltonian systems and their solutions in a systematic way. This …

The most well-known methods for the exact analysis of boundary value problems for linear
PDEs are the methods of (a) classical transforms,(b) images, and (c) Green's function …

A rigorous methodology for the analysis of initial-boundary value problems on the half-line,
is applied to the nonlinear § (NLS), to the sine-Gordon (sG) in laboratory coordinates, and to …

Assuming that the solution q (x, t) of the nonlinear Schrödinger equation on the half-line
exists, it has been shown in Fokas (2002 Commun. Math. Phys. 230 1–39) that q (x, t) can be …

In this paper, we address the problem of Yang-Baxter integrability of doubled quantum
circuit of qubits (spins 1/2) with open boundary conditions where the two circuit replicas are …

We consider the nonlinear Schrödinger (NLS) equation in the variable q(x,t) with both x and t
in 0,∞). We assume that q(x,0)=u(x) and q(0,t)=v(t) are given, that u(0)=v(0), and that u(x) …

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

We consider the one-dimensional focusing nonlinear Schrödinger equation (NLS) with a
delta potential and even initial data. The problem is equivalent to the solution of the …

A bstract ABJM theory in the presence of a half-BPS domain wall is dual to the D2-D4 probe
brane system with nonzero worldvolume flux. The ABJM domain wall was recently shown to …

We classify all regular solutions of the Yang-Baxter equation of eight-vertex type. Regular
solutions correspond to spin chains with nearest-neighbor interactions. We find a total of four …