On the variational interpretation of the discrete KP equation

Raphael Boll; Matteo Petrera; Yuri B. Suris

On the variational interpretation of the discrete KP equation

Mathematical Physics 2019-11-11 v1 math.MP Symplectic Geometry Exactly Solvable and Integrable Systems

Authors: Raphael Boll , Matteo Petrera , Yuri B. Suris

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

discrete KP equation variational structure pluri-Lagrangian formulation cubic lattice root lattice Euler-Lagrange equations

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@article{arxiv.1506.00729,
  title  = {On the variational interpretation of the discrete KP equation},
  author = {Raphael Boll and Matteo Petrera and Yuri B. Suris},
  journal= {arXiv preprint arXiv:1506.00729},
  year   = {2019}
}

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24 pages

On the variational interpretation of the discrete KP equation

Abstract

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