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On the Variational Interpretation of the Discrete KP Equation

In: Advances in Discrete Differential Geometry

Author

Listed:
  • 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)

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.

Suggested Citation

  • Raphael Boll & Matteo Petrera & Yuri B. Suris, 2016. "On the Variational Interpretation of the Discrete KP Equation," Springer Books, in: Alexander I. Bobenko (ed.), Advances in Discrete Differential Geometry, pages 379-405, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-50447-5_12
    DOI: 10.1007/978-3-662-50447-5_12
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