Recursion operators for KP, mKP and harry DYM hierarchies

Abstract

In this paper, we give a unified construction of the recursion operators from the Lax representation for three integrable hierarchies: KadomtsevPetviashvili (KP), modified KadomtsevPetviashvili (mKP) and Harry Dym under n-reduction. This shows a new inherent relationship between them. To illustrate our construction, the recursion operator are calculated explicitly for 2-reduction and 3-reduction. © J. Cheng, L. Wang and J. He.