We describe a general method of constructing nonlocal recursion operators for symmetries of PDEs. As an example, the cotangent equation to the 3D rdDym equation \(u_{yt} = u_xu_{xy} - u_yu_{xx}\) is considered for which two mutually inverse operators are found. The exposition includes a rigorous criterion to check the hereditary property of nonlocal recursion operators.

中文翻译：

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rdDym 方程余切覆盖中的递归算子

我们描述了为偏微分方程的对称性构造非局部递归算子的一般方法。例如，考虑到 3D rdDym 方程\(u_{yt} = u_xu_{xy} - u_yu_{xx}\)的余切方程，其中找到了两个互逆算子。该说明包括一个严格的标准来检查非局部递归运算符的遗传属性。