Second-order integrable Lagrangians and WDVV equations
Tóm tắt
We investigate the integrability of Euler–Lagrange equations associated with 2D second-order Lagrangians of the form
$$\begin{aligned} \int f(u_{xx},u_{xy},u_{yy})\ \mathrm{d}x\mathrm{d}y. \end{aligned}$$
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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