论文标题
多维集成方程的拉格朗日扩展。 I.五维市场
Lagrangian extensions of multi-dimensional integrable equations. I. The five-dimensional Mart{\'ı}nez Alonso--Shabat equation
论文作者
论文摘要
我们研究5dMartínezAlonso--Shabat方程的Lagrangian扩展$ \ MATHCAL {E} $ \ begin {qore*} u_ {yz {yz} = u_ {tx}+u_y \ u_y \，u_ {XS}}}}} -u_x} -u_x \，u_ _ {ys ys and} $ \ mathcal {t^*e} $。我们描述了其对称性的谎言代数结构（恰好是非常普遍的，并用变形来描述），并为对称性构建了两个递归操作员的家族。每个家庭都取决于两个参数。我们证明，第一家族的所有操作员都是遗传性的，但在Nijenhuis Bracket的意义上不兼容。我们还构建了两个新的参数宽松对，取决于未知函数的高阶衍生物。
We study a Lagrangian extension of the 5d Martínez Alonso--Shabat equation $\mathcal{E}$ \begin{equation*} u_{yz}=u_{tx}+u_y\,u_{xs}-u_x\,u_{ys} \end{equation*} that coincides with the cotangent equation $\mathcal{T^*E}$ to the latter. We describe the Lie algebra structure of its symmetries (which happens to be quite nontrivial and is described in terms of deformations) and construct two families of recursion operators for symmetries. Each family depends on two parameters. We prove that all the operators from the first family are hereditary, but not compatible in the sense of the Nijenhuis bracket. We also construct two new parametric Lax pairs that depend on higher-order derivatives of the unknown functions.
