论文标题
二阶可集成的拉格朗日和WDVV方程
Second-order integrable Lagrangians and WDVV equations
论文作者
论文摘要
我们研究了与形式的2D二阶拉格朗日相关联的Euler-lagrange方程的集成性\ begin {qore*} \ int f（u_ {xx}，u_ {xy}，u_ {yy}）\ dxdy。 \ end {equation*}通过得出拉格朗日密度$ f $的集成性条件，通过基本函数表达的可集成拉格朗日的示例，构建了jacobi theta函数和差异。建立了二阶Lagrangians与WDVV方程的链接。还讨论了对3D二阶的Lagrangians的概括。
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.
