On the Lagrangian multiform structure of the extended lattice Boussinesq system

Abstract

The lattice Boussinesq (lBSQ) equation is a member of the lattice Gel'fand-Dikii (lGD) hierarchy, introduced in \cite{NijPapCapQui1992}, which is an infinite family of integrable systems of partial difference equations labelled by an integer $N$, where $N=2$ represents the lattice Korteweg-de Vries (KdV) system, and $N=3$ the Boussinesq system. In \cite{Hiet2011} it was shown that, written as three-component system, the lBSQ system allows for extra parameters which essentially amounts to building the lattice KdV inside the lBSQ. In this paper we show that, on the level of the Lagrangian structure, this boils down to a linear combination of Lagrangians from the members of the lGD hierarchy as was established in \cite{LobbNijGD2010}. The corresponding Lagrangian multiform structure is shown to exhibit a `double zero' structure.

arXiv comment10 pages, 0 figures Accepted version, formatted in accordence with the publication template

References in corpus (9)

• Classification of integrable equations on quad-graphs. The consistency approach
• Boussinesq-like multi-component lattice equations and multi-dimensional consistency
• Lagrangian multiforms and multidimensional consistency
• Lagrangian multiform structure for the lattice Gel'fand-Dikii hierarchy
• Soliton Taxonomy for a Modification of the Lattice Boussinesq Equation
• An integrable multicomponent quad equation and its Lagrangian formulation
• Variational symmetries and Lagrangian multiforms
• Lagrangian 3-form structure for the Darboux system and the KP hierarchy
• A Variational Principle for Discrete Integrable Systems

Cited by in corpus (2)

• Lagrangian multiform structure of discrete and semi-discrete KP systems
• On the geometry of Lagrangian one-forms