Second-order integrable Lagrangians and WDVV equations

Abstract

We investigate integrability of Euler-Lagrange equations associated with 2D second-order Lagrangians of the form \begin{equation*} \int f(u_{xx},u_{xy},u_{yy})\ dxdy. \end{equation*} By deriving integrability conditions for the Lagrangian density $f$, examples of integrable Lagrangians expressible via elementary functions, Jacobi theta functions and dilogarithms are constructed. A link of second-order integrable Lagrangians to WDVV equations is established. Generalisations to 3D second-order integrable Lagrangians are also discussed.

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Cited by in corpus (3)

• Null Kähler geometry and isomonodromic deformations
• The Differential Geometry of the Orbit Space of Extended Affine Jacobi Group $A_1$
• Bi-Hamiltonian structures of WDVV-type