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 …

The aim of this work is to demonstrate the effectiveness of the extension theory of symmetric
operators in the investigation of the stability of standing waves for the nonlinear Schrödinger …

We present a framework to solve the open problem of formulating the inverse scattering
method (ISM) for an integrable PDE on a star-graph. The idea is to map the problem on the …

We investigate the existence and the uniqueness of NLS ground states of fixed mass on the
half-line in the presence of a point interaction at the origin. The nonlinearity is of power type …

We construct canonical quantum fields which propagate on a star graph modelling a
quantum wire. The construction uses a deformation of the algebra of canonical commutation …

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 …

We establish the scattering of solutions to the focusing mass supercritical nonlinear
Schrödinger equation with a repulsive Dirac delta potential i∂ t u+∂ x 2 u+ γ δ (x) u+| u| p …

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 …

The one-dimensional problem of N particles with contact interaction in the presence of a
tunable transmitting and reflecting impurity is investigated along the lines of the coordinate …