In this work we use the repeated application of the recursion operator to establish a new hierarchy of negative-order integrable KdV equations of higher orders. The concept of the inverse recursion operator allows us to develop this new hierarchy. The complete integrability of each equation is guaranteed via the use of the recursion operator. We show that the dispersion relations of this hierarchy follow an infinite geometric series. Multiple soliton solutions for each equation of the hierarchy are obtained.

中文翻译：

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递归运算符在负阶可积KdV方程的新层次结构中的重复应用

在这项工作中，我们使用递归运算符的重复应用来建立新的负阶可积KdV方程的新层次。逆递归运算符的概念使我们能够开发这种新的层次结构。通过使用递归运算符，可以保证每个方程的完全可积分性。我们表明，该层次结构的色散关系遵循无限的几何级数。对于该层次结构的每个方程，获得了多个孤子解。