Here we review the many aspects and distinct phenomena associated to quantum dynamics
on general graph structures. For so, we discuss such class of systems under the energy …

We review some recent results and announce some new ones on the problem of the
existence of ground states for the Nonlinear Schrödinger Equation on graphs endowed with …

We present an inverse scattering approach to defects in classical integrable field theories.
Integrability is proved systematically by constructing the generating function of the infinite set …

It is known that the initial‐boundary value problem for certain integrable Partial Differential
Equations (PDEs) on the half‐line with integrable boundary conditions can be mapped to a …

Abstract We revisit the Lieb–Liniger model for n bosons in one dimension with attractive
delta interaction in a half-space with diagonal boundary conditions. This model is integrable …

Recent work on purely transmitting'jump-defects' in the sine-Gordon model and other
relativistic field theories is extended to non-relativistic models. In all the cases investigated …

The classical sine-Gordon model permits integrable discontinuities, or jump-defects, where
the conditions relating the fields on either side of a defect are Bäcklund transformations …

A bstract We introduce the concept of multisymplectic formalism, familiar in covariant field
theory, for the study of integrable defects in 1+ 1 classical field theory. The main idea is the …

A bstract A systematic approach to Liouville integrable defects is proposed, based on an
underlying Poisson algebraic structure. The non-linear Schrödinger model in the presence …

We explore the phenomena of absorption/emission of solitons by an integrable boundary for
the focusing nonlinear Schrödinger equation on the half-line. This is based on the …