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: Kadomtsev-Petviashvili (KP), modified Kadomtsev-Petviashvili (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.

18 pages, accepted by Journal of Nonlinear Mathematical Physics(2010)

References in corpus (2)

• On recursion operators for elliptic models
• The geometry of recursion operators