The Recursion Operator of the Kadomtsev-Petviashvili Equation and the Squared Eigenfunctions of the Schrödinger Operator

The recursion operator of the Kadomtsev-Petviashvili equation is algorithmically derived. This recursion operator is the two-spatial-dimensional analogue of the Lenard operator of the Korteweg-deVries equation. It is also the “squared” eigenfunction operator of the time-dependent Schrödinger operator. The existence of the recursion operator suggests that the Kadomtsev-Petviashvili equation is a hi-Hamiltonian system.