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 …

We establish the algebraic origin of the following observations made previously by the
authors and coworkers:(i) A given integrable PDE in 1+ 1 dimensions within the Zakharov …

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 …

In recent years, new properties of space-time duality in the Hamiltonian formalism of certain
integrable classical field theories have been discovered and have led to their reformulation …

A bstract We study the integrable boundaries and crosscaps of classical sigma models. We
show that there exists a classical analog of the integrability condition and KT-relation of the …

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 …

Motivated by the notion of Lagrangian multiforms, which provide a Lagrangian formulation of
integrability, and by the results of the authors on the role of covariant Hamiltonian formalism …

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 …

We bring together aspects of covariant Hamiltonian field theory and of classical integrable
field theories in 1+ 1 dimensions. Specifically, our main result is to obtain for the first time the …

A bstract A new super-Bäcklund transformation for the N= 1 supersymmetric sinhGordon
equation is constructed. Based on this construction we propose a type-II integrable defect for …