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 define and illustrate the novel notion of dual integrable hierarchies, on the example of
the nonlinear Schrödinger (NLS) hierarchy. For each integrable nonlinear evolution …

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 …

Abstract Ideas from the theory of multisymplectic systems, introduced recently in integrable
systems by the author and Kundu to discuss Liouville integrability in classical field theories …

We consider the algebraic setting of classical defects in discrete and continuous integrable
theories. We derive the “equations of motion” on the defect point via the space-like and time …

A bstract A new integrable boundary for the classical nonlinear Schrödinger model is
derived by dressing a boundary with a defect. A complete investigation of the integrability of …

A bstract Type II integrable defects with more than one degree of freedom at the defect are
investigated. A condition on the form of the Lagrangian for such defects is found which …

The purpose of this paper is to extend the store of models able to support integrable defects
by investigating the two-dimensional Boussinesq nonlinear wave equation. As has been …

A folding process is applied to fused a^(1) _r defects to construct defects for the non-simply
laced affine Toda field theories of c^(1) _n, d^(2) _n and a^(2) _2n at the classical level …

By applying Darboux–Crum transformations to the quantum one-gap Lamé system, we
introduce an arbitrary countable number of bound states into forbidden bands. The …