This first introductory text to discrete integrable systems introduces key notions of
integrability from the vantage point of discrete systems, also making connections with the …

A Lagrangian multiform structure is established for a generalisation of the Darboux system
describing orthogonal curvilinear coordinate systems. It has been shown in the past that this …

We consider the discrete Boussinesq integrable system and the compatible set of differential
difference, and partial differential equations. The latter not only encode the complete …

We establish an infinite family of solutions in terms of elliptic functions of the lattice
Boussinesq systems by setting up a direct linearisation scheme, which provides the solution …

It is shown that the Zakharov–Mikhailov (ZM) Lagrangian structure for integrable nonlinear
equations derived from a general class of Lax pairs possesses a Lagrangian multiform …

Abstract The lattice Gel'fand–Dikii hierarchy was introduced by Nijhoff et al (1992 Inverse
Problems 8 597–621) as the family of partial difference equations generalizing to higher …

Based on the direct linearization framework of the discrete Kadomtsev–Petviashvili-type
equations presented in the work of Fu & Nijhoff (Fu W, Nijhoff FW. 2017 Direct linearizing …

The lattice Boussinesq (lBSQ) equation is a member of the lattice Gel'fand-Dikii (lGD)
hierarchy, introduced in [17], which is an infinite family of integrable systems of partial …

The interplay between the symmetries of compatible discrete and continuous integrable
systems in two dimensions is investigated. Master and higher symmetries for certain …

A symmetry reduction of the lattice modified Boussinesq system is studied. The full group of
Lie point symmetries of the relevant system is retrieved and certain group invariant solutions …