In this worksheet we symbolically construct the formal inverse of the total derivative operator and use it to construct the recursion operator for the higher-order symmetries of the KdV equation. Using this recursion operator we generate the first 5 generalized symmetries of the KdV equation and verify that they all commute.
PDF and Maple worksheets can be downloaded from the links below.
Anderson, Ian M., "Higher Order Symmetries of the KdV Equation" (2012). Research Vignettes. Paper 2.