On the Variational Interpretation of the Discrete KP Equation

Raphael Boll (), Matteo Petrera () and Yuri B. Suris ()
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Raphael Boll: Technische Universität Berlin, Inst. für Mathematik
Matteo Petrera: Technische Universität Berlin, Inst. für Mathematik
Yuri B. Suris: Technische Universität Berlin, Inst. für Mathematik

A chapter in Advances in Discrete Differential Geometry, 2016, pp 379-405 from Springer

Abstract: Abstract We study the variational structure of the discrete Kadomtsev-Petviashvili (dKP) equation by means of its pluri-Lagrangian formulation. We consider the dKP equation and its variational formulation on the cubic lattice $$\mathbb Z^{N}$$ as well as on the root lattice $$Q(A_{N})$$ . We prove that, on a lattice of dimension at least four, the corresponding Euler-Lagrange equations are equivalent to the dKP equation.

Keywords: Root Lattice; Elementary Cell; Cyclic Permutation; Exterior Derivative; White Triangle (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-662-50447-5_12

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DOI: 10.1007/978-3-662-50447-5_12

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