58 citations · 142 across the 7 of their papers we have counts for
7 papers
Constructing Initial Value Spaces of Lattice Equations
Nalini Joshi, Sarah Lobb, Matthew Nolan
In this paper, we examine the space of initial values for integrable lattice equations, which are lattice equations classified by Adler {\em et al} (2003), known as ABS equations.…
Singular dynamics of a -difference Painlevé equation in its initial-value space
Nalini Joshi, Sarah Lobb
We construct the initial-value space of a -discrete first Painlevé equation explicitly and describe the behaviours of its solutions in this space as , with pa…
A Variational Principle for Discrete Integrable Systems
Sarah B. Lobb, Frank W. Nijhoff
For integrable systems in the sense of multidimensional consistency (MDC) we can consider the Lagrangian as a form, which is closed on solutions of the equations of motion. For 2-d…
An integrable multicomponent quad equation and its Lagrangian formulation
J. Atkinson, S. B. Lobb, F. W. Nijhoff
We present a hierarchy of discrete systems whose first members are the lattice modified Korteweg-de Vries equation, and the lattice modified Boussinesq equation. The N-th member in…
Discrete-time Calogero-Moser system and Lagrangian 1-form structure
Sikarin Yoo-kong, Sarah Lobb, Frank Nijhoff
We study the Lagrange formalism of the (rational) Calogero-Moser (CM) system, both in discrete time as well as in continuous time, as a first example of a Lagrange 1-form structure…
On the Lagrangian formulation of multidimensionally consistent systems
Pavlos Xenitidis, Frank Nijhoff, Sarah Lobb
Multidimensional consistency has emerged as a key integrability property for partial difference equations (PEs) defined on the "space-time" lattice. It has led, among other majo…
Lagrangian multiforms and multidimensional consistency
Sarah Lobb, Frank Nijhoff
We show that well-chosen Lagrangians for a class of two-dimensional integrable lattice equations obey a closure relation when embedded in a higher dimensional lattice. On the basis…