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This article is cited in 20 scientific papers (total in 20 papers)
An integrable multicomponent quad-equation and its Lagrangian formulation
J. Atkinsona, S. B. Lobbb, F. W. Nijhoffc a University of Sydney, Sydney, Australia
b La Trobe University, Melbourne, Australia
c University of Leeds, Leeds, UK
Abstract:
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 the hierarchy is an $N$-component system defined on an elementary plaquette in the two-dimensional lattice. The system is multidimensionally consistent, and we obtain a Lagrangian that respects this feature, i.e., has the desirable closure property.
Keywords:
integrable system, discrete equation, reduction, Lagrange formulation, variational principle.
Received: 25.04.2012
Citation:
J. Atkinson, S. B. Lobb, F. W. Nijhoff, “An integrable multicomponent quad-equation and its Lagrangian formulation”, TMF, 173:3 (2012), 363–374; Theoret. and Math. Phys., 173:3 (2012), 1644–1653
Linking options:
https://www.mathnet.ru/eng/tmf8350https://doi.org/10.4213/tmf8350 https://www.mathnet.ru/eng/tmf/v173/i3/p363
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