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Lagrangian multiform structure for the lattice KP system

S B Lobb et al 2009 J. Phys. A: Math. Theor. 42 472002 (11pp)   doi: 10.1088/1751-8113/42/47/472002  Help

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S B Lobb1, F W Nijhoff1 and G R W Quispel2
1 Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, UK
2 Department of Mathematics and Statistics, La Trobe University, Victoria 3086, Australia

Abstract. We present a Lagrangian for the bilinear discrete KP (or Hirota–Miwa) equation. Furthermore, we show that this Lagrangian can be extended to a Lagrangian 3-form when embedded in a higher dimensional lattice, obeying a closure relation. Thus we establish the multiform structure as proposed in Lobb and Nijhoff (2009 J. Phys. A: Math. Theor. 42 454013) in a higher dimensional case.

PACS numbers: 45.20.Jj, 02.30.Ik, 04.20.Fy

Mathematics Subject Classification: 39A99, 49N99, 35Q51

Print publication: Issue 47 (27 November 2009)
Received 29 June 2009
Published 4 November 2009

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